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Concept# Electron cyclotron resonance

Summary

Electron cyclotron resonance (ECR) is a phenomenon observed in plasma physics, condensed matter physics, and accelerator physics. It happens when the frequency of incident radiation coincides with the natural frequency of rotation of electrons in magnetic fields. A free electron in a static and uniform magnetic field will move in a circle due to the Lorentz force. The circular motion may be superimposed with a uniform axial motion, resulting in a helix, or with a uniform motion perpendicular to the field (e.g., in the presence of an electrical or gravitational field) resulting in a cycloid. The angular frequency (ω = 2πf ) of this cyclotron motion for a given magnetic field strength B is given (in SI units) by
:\omega_\text{ce} = \frac{eB}{m_\text{e}}.
where e is the elementary charge and m is the mass of the electron. For the commonly used microwave frequency 2.45 GHz and the bare electron charge and mass, the resonance condition is

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This thesis focuses on the physics of suprathermal electrons generated by electron cyclotron (EC) waves in tokamak plasmas, which play an important role in the physics of current drive and energetic particle-driven instabilities. The suprathermal electron dynamics and their effect on the plasma stability have been experimentally studied utilizing high power EC waves, in the TCV tokamak of the Swiss Plasma Center at EPFL, Switzerland. A hard X-ray diagnostic, which measures the bremsstrahlung radiation of the suprathermal electrons in radial and energy spaces, has been mainly used for the analysis, and the measurement has been compared to an estimation made by Fokker-Planck modeling coupled with a hard X-ray synthetic diagnostic. In order to study the response of the suprathermal electrons to ECCD, ECCD modulation discharges have been developed. The time evolution of the hard X-ray profiles has been measured using coherent averaging techniques in order to observe the creation and relaxation of suprathermal electrons. Time-dependent Fokker-Planck modeling coupled with the hard X-ray synthetic diagnostic has been used to compare the experimental and simulation results, with various suprathermal electron transport models. A dependency of the radial transport of suprathermal electrons on the EC wave power has been demonstrated and a possibility of EC wave scattering has been addressed. The effect of the suprathermal electron population on the plasma stability has been studied, and in particular the destabilization and dynamics of the electron fishbone mode. The response of hard X-ray profiles to the internal kink mode has been observed directly by the hard X-ray diagnostic for the first time, at the frequency of the mode. The experimental evidence and a solution of a linear fishbone dispersion relation coupled to the Fokker-Planck modeling demonstrate the role of suprathermal electrons in destabilizing the fishbone mode and in particular the interaction of trapped electrons with the mode. This work provides the framework for a comprehensive understanding of the physics of suprathermal electrons related to ECCD, and explains how ECCD-generated suprathermal electrons behave in real and velocity spaces, and how they interact with and are redistributed by the MHD mode.

In magnetic confinement devices, the inhomogeneity of the confining magnetic field along a magnetic field line generates the trapping of particles (with low ratio of parallel to perpendicular velocities) within local magnetic wells. One of the consequences of the trapped particles is the generation of a current, known as the bootstrap current (BC), whose direction depends on the nature of the magnetic trapping. The BC provides an extra contribution to the poloidal component of the confining magnetic field. The variation of the poloidal component produces the alteration of the winding of the magnetic field lines around the flux surfaces quantified by the rotational transform ι. When ι reaches low rational values, it can trigger the generation of ideal MHD instabilities. Therefore, the BC may be responsible for the destabilisation of the configuration. This thesis is divided into two parts. In the first part, we present a self-consistent method to calculate the BC and assess its effect on equilibrium and stability in general 3D configurations. This procedure is applied to two reactor-size prototypes (both with plasma volumes ∼ 1000m3): a quasi-axisymmetric (QAS) system and a quasi helically symmetric (QHS) system with magnetic structures that develop BC in opposite directions. The BC increases with the plasma pressure, therefore its relevance is enhanced when dealing with reactor-level scenarios. The behaviour of both prototypes at reactor level values of β ≡ (kinetic plasma pressure)/(magnetic pressure) is assessed, as well as its alteration of the equilibrium and stability. In the QAS prototype, BC-consistent equilibria have been computed up to β = 6.7% and the configuration is shown to be stable up to β = 6.4%. Convergence of self-consistent BC calculations for the QHS case is achieved only up to β = 3.5%, but the configuration is unstable for β ≥ 0.6%. The relevance of symmetry breaking modes of the Fourier expansion of the confining magnetic field on the generation of BC is studied for each prototype. This proves the close relationship between magnetic structure and BC. Having established the potentially dangerous implication of the BC, principally, in reactor prototypes, a method to compensate its harmful effects is proposed in the second part of the thesis. It consists of the modelling of the current driven by externally launched ECWs within the plasma to compensate the effects of the BC. This method is flexible enough to allow the identification of the appropriate scenarios in which to generate the required CD depending on the nature of the confining magnetic field and the specific plasma parameters of the configuration. Both the BC and the CD calculations are included in a self-consistent scheme which leads to the computation of a stable BC+CD-consistent MHD equilibrium. This procedure is applied in this thesis to simulate the required CD to stabilise the QAS and QHS prototypes introduced in the first part. The estimation of the input power required and the effect of the driven current on the final equilibrium of the system is performed for several relevant scenarios and wave polarisations providing various options of stabilising driven currents. Several scenarios have been devised for each prototype in order to drive current at the appropriate location and with the desired direction. Different polarisations and launching conditions have been employed to this purpose. In particular, a HFS launched X2 ECW with an input power of 1.5MW has been shown to drive sufficient current to maintain the rotational transform below the critical value 2/3 at β = 6.4% for the QAS reactor. Correspondingly, in the QHS reactor, an X3-mode ECW of 100KW was sufficient to drive the current required to push the rotational transform below unity near the magnetic axis at β = 3%. Thus, stabilisation of BC-driven instabilities with externally launched ECWs has been achieved for both contrasting configurations. The method proposed in this thesis allows also the utilisation of EBW in the generation of CD. The possible advantages of EBCD for compensation studies are described as well as their possible application to the two prototypes under consideration. The BC+CD procedure is particularly interesting to investigate new magnetic geometries as potential candidates for fusion reactors. With this numerical tool, it is possible to assess the implications of their consistent BC when operating at reactor level. It also allows to quantify how much power would be required to maintain the system MHD stable in these circumstances. Nevertheless, this method is flexible enough to be applicable to any configuration.