# J. Vaclavik's research while affiliated with École Polytechnique Fédérale de Lausanne and other places

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## Publications (209)

Collisionless microtearing modes have recently been found linearly unstable in sharp temperature gradient regions of large aspect ratio tokamaks. The magnetic drift resonance of passing electrons has been found to be sufficient to destabilise these modes above a threshold plasma
β. A global gyrokinetic study, including both passing electrons as wel...

Unstable collisional MicroTearing Mode (MTMs) have been found in experiments of high-β Spherical Tokamaks and are believed to be driven by drift resonance of trapped electrons. It has been recently shown that at large aspect ratio, the magnetic drift resonance of highly passing electrons is a minimal mechanism to drive the collisionless MTM unstabl...

Linear full radius gyrokinetic calculations show the existence of unstable microtearing modes (MTMs) in purely collisionless, high temperature, large aspect ratio tokamak plasmas. The present study takes into account fully gyrokinetic highly passing ions and electrons. The global 2-D structures of the collisionless mode with full radius coupling of...

In this work, role of nonadiabatic untrapped electrons in the context of a global ion temperature gradient driven mode has been investigated. In past studies, untrapped electrons have been assumed to be able to respond "instantaneously" to a disturbance. It is proposed that such adiabatic electron models should be reexamined for two important reaso...

The heating of toroidal plasmas by resonant absorption of Alfvén waves is considered in the framework of ideal MHD. A theory is developed which closely parallels that of ideal-MHD stability. Computations are performed by using the numerical methods known from stability theory. It is shown that the overall picture of Alfvén wave heating in a torus w...

An electron density gradient driven instability identified as the toroidal branch of the universal drift instability is studied using a global gyrokinetic model treating both electrons and ions fully nonadiabatically and valid at all orders in the ratio of the Larmor radius to the wavelength. The physics of the magnetic drift resonance, Landau reso...

Electrons whether adiabatic or non-adiabatic play important role in determining the stability properties of a global electrostatic mode. In the present analysis, the effect of non-adiabaticity of electrons with all its kinetic effects is investigated for ion temperature gradient driven mode in the presence of fast ions using a linear gyro-kinetic c...

It is believed that low frequency microinstabilities such as ion temperature gradient (ITG) driven modes and trapped electron modes (TEMs) are largely responsible for the experimentally observed anomalous transport via the ion and electron channels in a tokamak. In the present work, a comprehensive global linear gyrokinetic model incorporating full...

The effect of trapped electrons on the ion temperature gradient ITG mode in a regime where its wavelength is shorter than the conventional ITG mode k Li 1 has been studied. Such a mode propagates in the ion diamagnetic direction with a typical scale length k Li 1 and is termed as the short wavelength ITG SWITG mode. The effect of the trapped electr...

Alfvén waves in fusion plasmas play an important role in a number of situations. First, in Alfvén Wave Heating (AWH) schemes. Second, both theory and experiment have demonstrated the existence of Global Alfvén Eigenmodes (GAEs). GAEs have been observed in different tokamaks (PRETEXT, TCA, TEXTOR, etc.) and, more recently, in a stellarator (Wendelst...

The absorption of power is studied with fluid and gyrokinetic plasma models, when Alfvén resonances provide for a weak damping in a partially standing wave field. Examples chosen in slab and toroidal geometry show that the fluid predictions based on resonance absorption are generally very different from the Landau damping of mode-converted slow wav...

A new code is presented here, named Gyrokinetic SEmi-LAgragian (GYSELA) code, which solves 4D drift-kinetic equations for ion temperature gradient driven turbulence in a cylinder (r, θ, z). The code validation is performed with the slab ITG mode that only depends on the parallel velocity. This code uses a semi-Lagrangian numerical scheme, which exh...

A common feature of the Vlasov equation is that it develops fine-scale filamentation as time evolves, as observed, for example, in global nonlinear simulations of the ion-temperature-gradient instability. From a numerical point of view, it is not trivial to simulate nonlinear regimes characterized by increasingly smaller scales, which eventually be...

With the term microinstabilities, we indicate a class of plasma drift waves such as the ion temperature gradient (ITG) mode, the trapped electron mode (TEM), and the electromagnetic Alfvenic ion temperature gradient (AITG) mode. They are usually driven by spatial gradients in the plasma and they are held responsible for anomalous transport and enha...

Tokamaks with large pressure gradients (alpha(max)) formed in regions of weak magnetic shear are shown to be susceptible to novel, low-n, global, kinetic, electromagnetic modes with a toroidal mode number n in the range 2</=n</=12. For a weakly varying monotonic safety factor profile q with its minimum q(min)>1 on the magnetic axis and alpha(max) n...

A semi-Lagrangian code for the solution of the electrostatic drift-kinetic equations in straight cylinder configuration is presented. The code, CYGNE, is part of a project with the long term aim of studying microturbulence in fusion devices. The code has been constructed in such a way as to preserve a good control of the constants of motion, posses...

Linear, fully gyrokinetic, full radius (global), large aspect ratio studies of Alfvén-ion temperature gradient mode (AITG) or kinetic ballooning modes or beta-induced Alfvén eigenmodes considering only ``passing'' species is presented. Effects hitherto completely neglected in a full radius approach such as B||-fluctuations and the ones which have b...

Electrostatic microinstabilities in ion internal barrier (ITB) and H-mode discharges of the ASDEX Upgrade tokamak [O. Gruber, R. Arslanbekov, C. Atanasiu et al., Nucl. Fusion 41, 1369 (2001)] have been investigated with a full radius gyrokinetic code. The code models linear stability and includes the effect of an equilibrium radial electric field a...

Finite difference and finite element approximations of eigenvalue problems, under certain circumstances, exhibit spectral pollution, i.e. the appearance of eigenvalues that do not converge to the correct value when the mesh density is increased. In the present paper this phenomenon is investigated in a homogeneous case by means of discrete dispersi...

The aim of this paper is to report on recent advances made in global gyrokinetic simulations of ion temperature gradient (ITG) modes and other microinstabilities. The nonlinear development and saturation of ITG modes and the role of E x B zonal flows are studied with a global nonlinear deltaf formulation that retains parallel nonlinearity and thus...

Electromagnetic microinstabilities in tokamak plasmas are studied by means of a linear global eigenvalue numerical code. Ion dynamics is described by the gyrokinetic equation, so that finite ion Larmor radius effects are taken into account to all orders. Nonadiabatic electrons are included in the model, with passing particles described by the drift...

The effects of applied radial electric fields on the stability of ion temperature gradient (ITG) modes and trapped particle modes are investigated with a full radius gyrokinetic formulation in both axisymmetric and helically symmetric configurations. The validity of a simplified stabilization criterion often applied to experimental analysis (the sh...

Relying on the good agreement observed between the gyrokinetic PENN model and the low toroidal
mode number n damping measurements from JET, the stability of Alfvén eigenmodes (AEs) is
predicted for reactor relevant conditions. Full non-local wave-particle power transfers are computed
between global wavefields and alpha particles in an ITER refer...

The modelling of Alfvénic instabilities is discussed from the point of view of mode-conversion, showing how the development of the theory affects the predictions as the limitations of the models are gradually relaxed. Conventional tokamak plasmas are relatively well understood and are used for the case of a kinetic Alfvén eigenmode (AE) to assess t...

Strong electric fields generate an E×B rotation of the equilibrium plasma. Experiments have shown that this effect could lower the anomalous transport in tokamaks. The study of the effect of these flows on the linear stability of ion temperature gradient (ITG) modes has therefore been undertaken. The question is addressed solving the spectrum of th...

The quasilinear evolution of ion-acoustic turbulence induced by a constant current in a two-temperature plasma (Te>>Ti) is considered. The pertinent equations, which include both resonant and nonresonant wave-particle interactions, are discretized by a finite element method and solved numerically. It is shown first that the nonresonant interaction...

Alfven eigenmodes (AEs) with intermediate toroidal mode numbers are modelled using the global gyrokinetic PENN code to determine the stability of high performance tokamak discharges in the presence of energetic particles. A large plasma pressure and a weak magnetic shear in the core give rise to radially extended kinetic AEs, which are stabilized b...

In the scope of the study of low-frequency electrostatic microinstabilities in tokamak plasmas, attention has been focused on the effect of trapped ions. The ballooning transform has been applied to the gyrokinetic equation, for the case of a large aspect ratio plasma with circular magnetic surfaces. A new eigenvalue code has been developed to solv...

A solution to the full two-dimensional eigenvalue problem of electrostatic microinstabilities in a tokamak plasma is presented in the framework of gyrokinetic theory. The approach is the generalization of methods previously developed for a cylindrical system [S. Brunner and J. Vaclavik, Phys. Plasmas 5, 365 (1998)]. By solving the spectral problem...

Nitrogen pool boiling on a structured surface coated with an organic fibre net insulation in a narrow channel was studied experimentally. The samples tested were elements of the copper stabilizer of a high-current superconducting cable. All the experimental conditions were close to the real winding operation ones. Two types of net surface insulatio...

We present a fully-global linear gyrokinetic simulation code (GYGLES) aimed at describing the unstable spectrum of the ion-temperature-gradient modes in toroidal geometry. We formulate the Particle-In-Cell method with finite elements defined in magnetic coordinates, which provides excellent numerical convergence properties. The poloidal mode struct...

Multi-stage flash (MSF) distillation of seawater is an established technique for desalinating seawater in coastal arid countries. Although MSF distillers differ in design, size and capacity, their operation encompasses a number of standard processes which aim to overcome a performance difficulty or improve production efficiency. These processes aff...

Considering the spectral problem of microinstabilities in a curved system, methods for solving the global gyrokinetic equation are presented for the simple case of a cylindrical plasma. They prove to be efficient for computing the full unstable spectrum of ion temperature gradient ITG type modes and have shown to be applicable to the two-dimensiona...

Global gyrokinetic particle simulations have been used to search tokamak configurations which are stable again st the ion-temperature-gradient - driven (ITG) modes commonly held responsible for the core anomalous ion heat transport. The stable configurations are-characterized by strongly reduced or reversed del B drifts on the low-field side. Since...

Global Alfvén eigenmodes are studied using two different models for the plasma and the results compared with the instability threshold measured experimentally. Fluid-resistive models predict that continuum damped toroidicity induced Alfvén modes (TAE) are formed in the frequency range of the experimental instabilities, but using realistic values of...

Kinetic effects such as finite ion Larmor excursions and resonant Landau interactions are studied in the toroidicity Alfven eigenmode (TAE) range of frequencies. A new Alfven mode conversion mechanism is described taking place away from the resonances through toroidal mode coupling. It generates a group of kinetic Alfven eigenmodes (KAE) in the nei...

The spectrum of n = 0 Alfven modes is calculated analytically and numerically in cylindrical and toroidal geometries. It includes global Alfven eigenmodes (GAEs) and surface modes (SMs) of the fast magnetoacoustic wave. These modes are not induced by toroidicity. The n = 0 GAEs owe their existence to shear. The frequency spacing between different r...

We study finite pressure effects on the Ion Temperature Gradient (ITG) instabilities; these modes are stabilized when the magnetic field gradient is reversed at high beta [1]. This second stability regime for ITG modes is studied in details with a global linear gyrokinetic Particle-In-Cell code which takes the full toroidal MHD equilibrium data fro...

Maxwell's equations are solved in a toroidal axisymmetric plasma. The numerical method implemented in the PENN code is based on a formulation in terms of the electromagnetic potentials and a discretization with standard bilinear or bicubic Hermite finite elements. Two models for the dielectric tensor operator yield different physical problems, whic...

The global stability of toroidicity induced Alfvh eigenmodes (TAEs) in the presence of fast ions in realistic tokamak fusion-grade plasmas is analysed with a global, perturbative approach. Volume averaged fast particle betas for marginal stability are obtained and analysed for a wide range of plasma parameters such as the fast ion radial density pr...

A new code, SEMAL, has been developed which solves the linearized Vlasov-Maxwell wave equations to all orders in Larmor radii. Arbitrary density and temperature profiles as well as non-uniform magnetic fields are considered in slab geometry. The vacuum regions adjacent to the plasma slab are limited by perfectly conducting walls and contain an ante...

Kinetic theory is used to develop equations describing dynamics of small-amplitude electromagnetic perturbations in toroidal axisymmetric plasmas. The closed Vlasov-Maxwell equations are first solved for a hot stationary plasma using the expansion in the small parameter E,=~/L, where p is the Larmor radius and L a characteristic length scale of the...

A model based on the linearized Vlasov-Maxwell equations, taking into account the non-local interactions of particles due to their finite Larmor radii, has been developed. Assuming an inhomogeneous I-D slab plasma, Maxwellian equilibrium distribution functions and k(y) = 0, this model leads to a system of one first-order and two second-order integr...

The present status of the theory of plasma heating by low frequency waves is reviewed from a unified point of view based on the concept of the dielectric tensor operator.

An explicit expression for the local power absorption density in a uniformly-magnetized slab plasma is derived from the Vlasov-Maxwell equations, taking into account density and temperature gradients. Using a transformation to Lagrangian coordinates, the kinetic flux of energy due to particle streaming can be separated in a suitable way from the ac...

A number of features of Alfvén wave heating make it potentially attractive for use in large tokamak reactors. Among them are the availability and relatively low cost of the power supplies, the potential ability to act selectively on the current profile, and the probable absence of operational limits in size, fields or density. The physics of Alfvén...

A numerical code, SEAL, solving the full form of a second-order integrodifferential equation that describes electrostatic waves in a slab plasma is presented. No expansion in the smallness of the ion Larmor radius is made. The plasma may have arbitrary density and temperature profiles and is immersed in a nonuniform magnetic field. Only small magne...

Excitation of Alfvén waves in the TCA tokamak using an external antenna structure produces a radially inward propagating and strongly damped wave which is observable through its associated density oscillations. It is found to have the properties of the kinetic Alfvén wave predicted to be created by resonant mode conversion at shear Alfvén wave reso...

The quasilinear theory, the lowest order nonlinear theory of plasma turbulence is nowadays one of the most consolidated and useful theoretical tools for the investigation of several important problems in the domain of controlled nuclear fusion research. Perhaps, the best merit of quasilinear theory is that of reducing the complicated phenomenon of...

A new way is discussed to handle numerically the ion-ion hybrid resonance appearing in the cold plasma model for plasma heating in the ion-cyclotron range of frequency (ICRF). It is shown that this singularity can be correctly treated without introducing artificial and unphysical damping outside the resonance domain. This feature is particularly im...

Summary The generation of plasma current by means of electromagnetic waves in the lower-hybrid (LH) range of frequency in the presence
of an opposing d.c. electric field is examined within the context of a two-dimensional quasi-linear numerical model. This
model, implemented in the finite-element code ADLER, solves for the simultaneous evolution of...

A mechanism, in which the wave induced flux plays the key role, is proposed to explain the density rise observed during Alfvén wave heating in the TCA tokamak.

A general formulation of the local power absorption density is obtained from the Vlasov equation. An explicit expression is derived for a specific case in a two-dimensional geometry.

Two of the technically most developed numerical descriptions of radio frequency waves are discussed: global-wave and quasilinear codes. The numerical approaches are presented within the physical context. The techniques considered are different finite element methods ranging from cubic Hermite finite elements to the non-conforming “finite hybrid ele...

This paper presents numerical methods developed for the calculation of global wave solutions in cold plasmas, in connection with rf heating in the Alfvén and ion Cyclotron Range Frequency. Both one-dimensional and two-dimensional geometries are treated, with special emphasis on the toroidal geometry. A scheme based on a variational formulation and...

A 2-D finite-element evolution Fokker-Planck code, BACCHUS, is presented. The originally current-drive version and a more recent bounce-averaged version are discussed in some detail. A quasi-linear code, RUNAWAY, is also described, especially to elucidate the major difficulties arising when the wave-particle interaction is included in a self-consis...

A system of two second-order ordinary differential equations describing wave propagation in a hot plasma is solved numerically by the finite element method involving standard linear and cubic elements. Evanescent short-wavelength modes do not constitute a problem because of the variational nature of the method. It is straightforward to generalize t...

The equations of quasilinear theory are derived for a uniformly magnetized inhomogeneous plasma interacting with electromagnetic field fluctuations. The derivation avoids the use of the random phase approximation, and requires no assumption on the ratio of the Larmor radius to the fluctuation wavelength. These equations are used to obtain the trans...

Reviews recent developments in the theory of MHD waves in connection with radio-frequency heating in the Alfven wave and ion cyclotron ranges of frequencies (AWRF, ICRF). The account focuses on the discussion of full wave solutions and the oscillation spectra in bounded, generally inhomogeneous, plasmas. Original results are presented concerning fo...

The problem of quasilinear diffusion of plasma electrons, resonantly interacting with waves in lower-hybrid range of frequency launched from the exterior, is examined within a self-consistent one-dimensional homogeneous model. An analytical solution is obtained, which allows the derivation of a simple formula for the plasma current in terms of the...

Present experiments with ion-cyclotron heating are mainly devoted to study ion-cyclotron resonance heating of hydrogen and 3He in a deuterium plasma. However, for a thermonuclear fusion experiment this frequency range has the undesirable feature of turning into α-particle heating as soon as alpha particles are created. Because of the large Doppler...

It is shown that a small, low-phase-velocity part of a power source spectrum can strongly enhance the amount of the current generated in lower-hybrid current-drive experiments. A good agreement between the calculated and observed current is found. Permanent address: Department of Physics, Auburn University, Auburn, AL 36830, USA.

The spectrum of low-frequency, m= ±1 oscillations in a cold, collisionless, cylindrical plasma comprises the frequencies of the lowest radial eigenmodes and the surface modes of the fast magnetosonic wave, all the global eigenmodes of the Alfve´n wave (ion-cyclotron wave), and the Alfve´n continuum. The spectrum of a homogeneous, currentless plasma...

The present understanding (May 1983) of current drive by lower hybrid waves in Tokamak
plasmas is reviewed with particular stress on the theory. First, the "classical" model of Fisch and its variants are discussed in light of recent experimental data. It is argued that these simple models do not account for most of the features of the results obtai...