F. Villone

The linearized CREATE-L plasma response model for the control of current, position and shape in tokamaks

CREATE-L, a simple and reliable linearized plasma response model for the control of the plasma current, position and shape in tokamaks, is presented. The basic assumption made is that the plasma behaviour is described using three degrees of freedom, related to the total plasma current, internal inductance and poloidal beta. The state variables are the coil and plasma currents; the inputs are the applied voltages, whereas poloidal beta and internal inductance play the role of disturbances. The outputs are field and flux values and some basic plasma parameters. The model is tested against non-linear codes and validated via comparison with experimental results.

An Integral Formulation for the Electrodynamics of Metallic Carbon Nanotubes Based on a Fluid Model

An integral formulation to model, in the frequency domain, the electromagnetic response of three-dimensional (3-D) structures formed by metallic carbon nanotubes and conductors, within the framework of the classical electrodynamics, is described. The conduction electrons of the metallic nanotube are modeled as an infinitesimally thin cylindrical layer of compressible fluid, whose dynamics are described by means of the linearized hydrodynamic equations. The resulting integral equations are solved numerically by the finite element method using the facet elements and the null-pinv decomposition. The proposed formulation is applied to study carbon nanotube interconnects and dipole antennas and some related results are outlined. The solutions highlight the high-frequency effects due to the electron inertia and the fluid pressure. In particular, since the kinetic inductance matrix dominates over the magnetic one, proximity effects are negligible

Plasma response models for current, shape and position control in JET

Abstract This paper presents the features and the performance of the Joint European Torus (JET) plasma response models based on an upgraded version of the CREATE-L code. It takes into account a number of aspects, including an equivalent axisymmetric model of the iron core and the eddy currents induced in the passive structures. The input quantities are the poloidal field circuit currents (or voltages) and two parameters related to the plasma current density profile. The output quantities include the signals provided by the magnetic diagnostic system of JET (fields, fluxes and flux differences) as well as plasma current and shape. The equivalent axisymmetric model of JET and the plasma response models have been assessed on a set of JET pulses, by comparing the simulated open loop response of the magnetic measurements and the plasma shape to the experimental measurements. The electromagnetic analysis shows that the axisymmetric model of the iron is satisfactory. The linearized plasma response model provides a reliable base for the design and the assessment of a new current, shape and position control system in JET, and accurately predicts the growth rate of the vertical instability of an elongated JET plasma.

A transmission line model for metallic carbon nanotube interconnects

A transmission line (TL) model describing the propagation of electric signals along metallic single wall carbon nanotube (CNT) interconnects is derived in a simple and self-consistent way within the framework of the classical electrodynamics. The conduction electrons of metallic CNTs are modelled as an infinitesimally thin cylindrical layer of a compressible charged fluid with friction, moving in a uniform neutralizing background. The dynamic of the electron fluid is studied by means of the linearized hydrodynamic equations with the pressure assumed to be that of a degenerate spin-½ ideal Fermi gas. Transport effects due to the electron inertia, quantum fluid pressure and electron scattering with the ion lattice significantly influence the propagation features of the TL. The simplicity and robustness of the fluid model make the derivation of the TL equations more straightforward than other derivations recently proposed in the literature and provide simple and clear definitions of the per unit length (p.u.l.) TL parameters. In particular, this approach has provided a new circuit model that can be used effectively in the analysis of networks composed of CNT transmission lines and lumped elements. The differences and similarities between the proposed model and those given in the literature are highlighted. Copyright

Performance Comparison Between Metallic Carbon Nanotube and Copper Nano-Interconnects

This paper addresses the problem of scaling interconnects to nanometric dimensions in future very-large-scale integration applications. Traditional copper interconnects are compared to innovative interconnects made by bundles of metallic carbon nanotubes. A new model is presented to describe the propagation of electric signals along carbon nanotube (CNT) bundles, in the framework of the classical transmission line theory. A possible implementation of a future scaled microstrip based on CNT bundle is analyzed and compared to a conventional microstrip.

A New Circuit Model for Carbon Nanotube Interconnects With Diameter-Dependent Parameters

In this paper, a new circuit model for the propagation of electric signals along carbon nanotube interconnects is derived from a fluid model description of the nanotube electrodynamics. The conduction electrons are regarded as a 2-D charged fluid, interacting with the electromagnetic field produced by the ion lattice, the conduction electron themselves, and the external sources. This interaction may be assumed to be governed by a linearized Eulers equation, which provides the nanotube constitutive equation to be coupled to Maxwell equations. A derivation of a circuit model is then possible within the frame of the classical multiconductor transmission-line (TL) theory. The elementary cell of this TL model differs from those proposed in literature, due to the definition of the circuit variable corresponding to the voltage. When considering small nanotube radius, we obtain values for the kinetic inductance and quantum capacitance that are consistent with literature. These values are corrected here to take into account the influence of larger values of radius properly. Conversely, the value of the per unit length resistance is roughly half of the value usually adopted in literature. The multiconductor TL model is used to study the scaling law of the parameters with the number of carbon nanotubes in a bundle.

Advances in the physics basis for the European DEMO design

In the European fusion roadmap, ITER is followed by a demonstration fusion power reactor (DEMO), for which a conceptual design is under development. This paper reports the first results of a coherent effort to develop the relevant physics knowledge for that (DEMO Physics Basis), carried out by European experts. The program currently includes investigations in the areas of scenario modeling, transport, MHD, heating & current drive, fast particles, plasma wall interaction and disruptions.

Linearly perturbed MHD equilibria and 3D eddy current coupling via the control surface method

In this paper, a coupling strategy based on the control surface concept is used to self-consistently couple linear MHD solvers to 3D codes for the eddy current computation of eddy currents in the metallic structures surrounding the plasma. The coupling is performed by assuming that the plasma inertia (and, with it, all Alfven wave-like phenomena) can be neglected on the time scale of interest, which is dictated by the relevant electromagnetic time of the metallic structures. As is shown, plasma coupling with the metallic structures results in perturbations to the inductance matrix operator. In particular, by adopting the Fourier decomposition in poloidal and toroidal modes, it turns out that each toroidal mode can be associated with a matrix (additively) perturbing the inductance matrix that commonly describes the magnetic coupling of currents in vacuum. In this way, the treatment of resistive wall modes instabilities of various toroidal mode numbers and their possible cross-talk through the currents induced in the metallic structures can be easily studied.

Measurement of the open loop plasma equilibrium response in TCV

A new technique and results are presented for the estimation of the open loop frequency response of the plasma on TCV. Voltages were applied to poloidal field coils and the resulting plasma current, position and shape related parameters were measured. The results are compared with the CREATE-L model, and good agreement is confirmed. The results are a significant advance on previous comparisons with closed loop data, which were limited by the role of feedback in the system. A simpler circuit equation model has also been developed in order to understand the reasons for the good agreement and identify which plasma properties are important in determining the response. The reasons for the good agreement with this model are discussed. An alternative modelling method has been developed, combining features of both the theoretical and experimental techniques. Its advantage is that it incorporates well defined knowledge of the electromagnetic properties of the tokamak with experimental data to derive plasma related parameters. This new model provides further insight into the plasma behaviour.

A modern plasma controller tested on the TCV tokamak

A high-order, multivariable, modern plasma controller has been designed using H-infinity optimal control techniques and tested oil the Tokamak Configuration Variable (TCV) tokamak. An initial design for the control of the plasma current, position, and shape parameters is described. The design process was based on the CREATE-L linearized model of TCV, and the controller was implemented oil a digital processor. The results demonstrated that the required performance was delivered and the controller response was in good agreement with predictions using the model.