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

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## Publications (204)

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...

The performance of a modular helical antenna for Alfvén wave heating is analysed in the framework of 1-D cylindrical theory, including finite-frequency (i.e. Hall current) effects. It is shown that modes with either positive or negative helicity can be preferentially excited in the plasma by tilting the antenna with respect to the poloidal magnetic...

We present the application of the recent physics-conforming COOL method [2,4] to the eigenvalue problem of a cylindrical waveguide filled with unmagnetized plasma. Using the Fourier transform only along the waveguide and not in poloidal direction, this is a relevant test case for a numerical discretization method in two dimensions (radial and poloi...

A global plasma turbulence simulation code, ORB5, is presented. It solves the gyrokinetic electrostatic equations including zonal flows in axisymmetric magnetic geometry. The present version of the code assumes a Boltzmann electron response on magnetic surfaces. It uses a Particle-In-Cell (PIC), δf scheme, 3D cubic B-splines finite elements for the...

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...

Electron cyclotron resonance heating (ECRH) is a mature technology that has progressed constantly over a period of forty years, particularly as a tool in magnetic confinement fusion. As with other heating methods, this technique has seen a steady increase in the sophistication of its applications, from bulk heating through profile tailoring and fin...

On the Tokamak `a Configuration Variable (TCV), electron internal transport
barriers (eITBs) can be formed during a gradual evolution from a centrally
peaked to a hollow current profile while all external actuators are held constant.
The formation occurs rapidly (<τeE) and locally and, according to ASTRA
modelling, is consistent with the appearance...

Important ingredients of the advanced-tokamak route to fusion have been explored in depth in the Tokamak à Configuration Variable [ F. Hofmann, J. B. Lister, M. Anton et al., Plasma Phys. Controlled Fusion 36, B277 (1994) ] over the past two years. Using a uniquely powerful and flexible electron-cyclotron resonance heating (ECRH) system as the prim...

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 TCV tokamak ( R = 0.88 m, κ = 2.5, are produced at low normalized current using far off-axis EC heating (ECH) and ECCD to broaden the current profile. Third harmonic heating is used to heat the plasma center where the second harmonic is in cut-off. Both second and third harmonic heating are used to heat H-mode plasmas, at the edge and center, r...

The Tokamak Configuration Variable (TCV) tokamak (R = 0.88 m, a < 0.25 m, B < 1.54 T) programme is based on flexible plasma shaping and heating for studies of confinement, transport, control and power exhaust. Recent advances in fully sustained off-axis electron cyclotron current drive (ECCD) scenarios have allowed the creation of plasmas with high...

This paper presents experimental results on the accessibility and the properties of plasmas with improved confinement in TCV. First, the H-mode threshold power is measured in Ohmic plasmas. Above an Ohmic threshold density, the threshold power increases with the density. A lower threshold density is found when additional electron cyclotron heating...

This paper presents experimental results on the accessibility and the properties
of plasmas with improved confinement in TCV. First, the H-mode threshold
power is measured in Ohmic plasmas. Above an Ohmic threshold density, the
threshold power increases with the density. A lower threshold density is found
when additional electron cyclotron heating...

In noninductively driven discharges, 0.9 MW second harmonic (X2) off-axis co-electron cyclotron current drive deposition is combined with 0.45 MW X2 central heating to create an electron internal transport barrier (eITB) in steady plasma conditions resulting in a 1.6-fold increase of the confinement time (tau(Ee)) over ITER-98L-mode scaling. The eI...

The physics of tokamak plasmas, in which electrons are heated by electron cyclotron heating (ECH) and whose current is driven by electron cyclotron current drive (ECCD), is investigated in this paper together with applications on tokamak à configuration variable (TCV) using modifications of the pressure and current profiles to improve the operation...

Sawtooth inversion radii and profile peaking factors of a large variety of ohmic
and ECH heated L mode plasmas, including elongations up to 2.6 and triangularities between
-0.5 and 0.75, have been investigated in the TCV tokamak. In ohmic plasmas, normalized
inversion radii and electron temperature profile peaking factors (corrected for sawtooth...

The operating space of the TCV tokamak has been extended to higher elongation, κ = 2.8, and higher normalized current, IN = IP/aB = 3.6 MA/mT, than were previously attainable. This has been achieved by optimizing the parameters of the vertical position control system and by optimizing the plasma shape. Experimental current and beta limits were foun...

The TCV tokamak (R = 0.88 in, a < 0.25 in, BT < 1.54 T) is equipped with six 0.5 MW gyrotron sources operating at 82.7 GHz for second harmonic X mode ECH. By distributing the ECCD current sources over the discharge cross section, fully driven stationary plasmas with I-p = 210 kA, n(e0) = 2 x 10(19) m(-3), T-e0 approximate to 4 keV, were obtained fo...

First global linear study of electrostatic drift waves in two realistic quasisymmetric configurations, namely the Quasi-Axially symmetric Stellarator with three fields periods (QAS3) [P. Garabian and L. P. Ku, Phys. Plasma 6, 645 (1999)] and the Helically Symmetric eXperiment (HSX) [F. S. B. Anderson et al., Trans. Fusion Technol. 27, 273 (1995)],...

Fully noninductive, steady-state electron cyclotron current drive (ECCD) has been demonstrated for the first time in experiments carried out in the tokamak à configuration variable (TCV) [O. Sauter et al., Phys. Rev. Lett. 84, 3322 (2000)]. By appropriately distributing six 0.45 MW ECCD sources over the discharge cross section, fully noninductive,...

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...

Experiments with high-power electron cyclotron heating (ECH) and current drive (ECCD) in the TCV tokamak are discussed. Power up to 2.7 MW from six gyrotrons is delivered to the tokamak at the second-harmonic frequency (82.7 GHz) in X-mode. The power is transmitted to the plasma by six independent launchers, each equipped with steerable mirrors tha...

A steady-state, fully noninductive plasma current has been sustained for the first time in a tokamak using electron cyclotron current drive only. In this discharge, 123 kA of current have been sustained for the entire gyrotron pulse duration of 2 s. Careful distribution across the plasma miner radius of the power deposited from three 0.5-MW gyrotro...

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...

A two-dimensional PIC code aimed at the investigation of electron-cyclotron beam instabilities in gyrotrons and their effects on the beam quality is presented. The code is based on recently developed techniques for handling charge conservation and open boundaries and uses all electromagnetic field which is decomposed in its transverse magnetic (TM)...

Extensive simulations are performed to investigate effects of electron cyclotron instabilities on the gyrotron beam quality, using two-dimensional axisymmetric particle-in-cell (PIG) codes. Both electrostatic and electromagnetic models, as well as realistic geometries of the gyrotron, are considered. It is found that a large beam density can lead t...

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...

The method of inequalities is applied to the of design a robust PI controller for a multi-stage flash (MSF) desalination plant. The method takes into account the given variations in process gain, time delay and time constant (Kp, τd and τ) of the transfer function models. The performance of the closed loop system is evaluated for different operatin...

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...

A program environment is presented that enables a co-operative design of high-technology products demanding interdisciplinary computer simulations for their optimisation. The system includes a multi-site, multi-machine, distributed data manager accessible by a data monitor. A client-server concept supports the user of massively parallel machines. T...

A two-dimensional PIC code aimed at the investigation of electron-cyclotron beam instabilities in gyrotrons and their effects on the beam quality is presented. The code is based on recently developed techniques for handling charge conservation and open boundaries. It has been implemented on the massively parallel computer CRAY T3D. First results sh...

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...

The direct sparse matrix solver is based on a domain decomposition technique to achieve data and work parallelization. Geometries that have long and thin structures are specially efficiently tractable with this solver, provided that they can be decomposed mainly in one direction. Due to the separation of the algorithm into a factorization stage and...

Exergy provides the cost accounting equations for allocating energy in any plant. Sets of complex auxiliary equations can be derived to allocate energy cost for each plant item and system. Here a simplified alternate method has been developed utilizing the First Law of Thermodynamics with consideration of the cost factors to distribute fuel in dual...

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...

Dynamical chaos is produced by the interaction between plasma particles and two electrostatic waves. Experiments performed in a linear magnetized plasma and a 1D particle-in-cell simulation agree qualitatively: above a threshold wave amplitude, ion stochastic diffusion and heating occur on a fast time scale. Self-consistency appears to limit the ex...

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...

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...

The system of two partial differential equations describing, on the basis of a cold plasma model, the propagation of low-frequency waves in an axisymmetric, current-carrying torus is shown to be singular in a two-dimensional domain of the independent variables. Regularized by means of a causal damping the singular domain becomes a resonantly absorb...

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 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...

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...

The antenna structure in the TCA tokamak is phased to excite preferentially Alfven waves with known toroidal and poloidal wave numbers. Surprisingly, the loading spectrum includes both discrete and continuum modes with poloidal wave numbers incompatible with the antenna phasing. These additional modes, which are important for our heating experiment...

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.