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Concept# Magnetic confinement fusion

Summary

Magnetic confinement fusion is an approach to generate thermonuclear fusion power that uses magnetic fields to confine fusion fuel in the form of a plasma. Magnetic confinement is one of two major branches of fusion energy research, along with inertial confinement fusion. The magnetic approach began in the 1940s and absorbed the majority of subsequent development.
Fusion reactions combine light atomic nuclei such as hydrogen to form heavier ones such as helium, producing energy. In order to overcome the electrostatic repulsion between the nuclei, they must have a temperature of tens of millions of degrees, creating a plasma. In addition, the plasma must be contained at a sufficient density for a sufficient time, as specified by the Lawson criterion (triple product).
Magnetic confinement fusion attempts to use the electrical conductivity of the plasma to contain it through interaction with magnetic fields. The magnetic pressure offsets the plasma pressure. Developing a suitable arra

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PHYS-424: Plasma II

This course completes the knowledge in plasma physics that students have acquired in the previous two courses, with a discussion of different applications, in the fields of magnetic confinement and controlled fusion, astrophysical and space plasmas, and societal and industrial applications.

PHYS-445: Nuclear fusion and plasma physics

The goal of the course is to provide the physics and technology basis for controlled fusion research, from the main elements of plasma physics to the reactor concepts.

PHYS-731: Magnetic confinement

To provide an overview of the fundamentals of magnetic confinement (MC) of plasmas for fusion.The different MC configurations are presented, with a description of their operating regimes.The basic elements of particle & energy transport, of plasma-wall interaction & of burning plasma are introduced.

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Fusion power is a proposed form of power generation that would generate electricity by using heat from nuclear fusion reactions. In a fusion process, two lighter atomic nuclei combine to form a heavi

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Nuclear fusion is a reaction in which two or more atomic nuclei, usually deuterium and tritium (hydrogen variants), are combined to form one atomic nuclei and subatomic particles (neutrons or prot

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Thermonuclear controlled fusion is a promising answer to the current energy and climate issues, providing a safe carbon-free source of energy which is virtually inexhaustible. In magnetic confinement thermonuclear fusion based on tokamak reactors, hydrogen fuel in the state of plasma is confined using a system of external and self-generated magnetic fields. This thesis contributes to the development of magnetic confinement fusion research by applying techniques derived from control engineering to designing magnetic controllers for tokamak plasmas. Specifically, a new design for feedback control of plasma shape and position in the TCV tokamak is provided, and its efficacy is studied in dedicated simulations and experiments.Elongated plasmas lead to improved plasma performance in tokamaks, which is key to sustaining fusion conditions in reactors. The required magnetic field for shaping the plasma column however results in an unstable equilibrium that makes feedback control of the vertical plasma position mandatory. Active stabilization of the axisymmetric plasma vertical instability is a standard feature of elongated tokamaks and will be a fundamental feature in the ITER magnetic control system, since a loss of vertical control and the subsequent plasma disruption can lead to unacceptable heat loads on the plasma facing components.The TCV tokamak is the ideal benchmark for investigating the effect of plasma shaping on tokamak physics and performance, with its system of 16 independently powered poloidal field coils and a vessel with an elongated cross section. Shape and position control are coupled problems in TCV as they share the same poloidal field coils as actuators, requiring a multivariable approach to designing magnetic controllers.In this thesis, controller design for TCV is based on a model for the coupled plasma-vessel-coils electromagnetic dynamics: the RZIp model. In this axisymmetric model, the plasma current distribution is fixed but is free to move radially and vertically in the poloidal plane of a toroidal reference frame. An extension to this model is suggested, relaxing the assumption of rigid displacement in the radial direction to include plasma shape deformation and leading to a semi-rigid RZIp model which better fits numerical equilibria.An improvement to the existing algorithm for shape and position control in TCV is then proposed. In this new approach, tuning of the plasma position controller, in charge of vertical stabilization, can be performed independently of the shape controller, which itself acts on a stable system. Static decoupling is achieved and the shape controller is designed on the basis of an improved model for the plasma deformation, which includes the plasma contribution to the static magnetic flux perturbation. Simulations in closed loop with the RZIp model are provided to evaluate several optimized schemes.Finally, the vertical controller is optimized including the plasma dynamics as part of the controller design. Structured H-infinity, extending classical H-infinity to fixed-structure control systems, is applied to obtain a controller using all available coils for position control, and in particular a coil combination optimized for vertical stabilization. Closed-loop performance improvement is demonstrated in dedicated TCV experiments, confirming the simulation results and paving the way for the routine integration of the optimized position and shape controller in TCV discharges.

Microturbulence driven by plasma instabilities is in most cases the dominant cause of heat and particle loss from the core of magnetic confinement fusion devices and therefore presents a major challenge in achieving burning plasma conditions. The role of passing electron dynamics in turbulent transport driven by ion-scale microinstabilities, in particular Ion Temperature Gradient (ITG) and Trapped Electron Mode (TEM) instabilities, has been given relatively little attention. In first approximation, these particles, which are highly mobile along the confining magnetic field, are assumed to respond adiabatically to the low frequency ion-scale modes. However, near mode rational surfaces (MRSs), the non-adiabatic response of passing electrons becomes important and can no longer be neglected.
This non-adiabatic electron response actually has a destabilising effect and leads to generation of fine-structures located at the MRSs of each eigenmode. This thesis focuses on the effects of non-adiabatic response of passing electrons in tokamak core turbulence.
One such effect of non-adiabatic passing electrons that is of particular interest to this work is the self-interaction mechanism. It is essentially a process by which a microinstability eigenmode that is extended along the direction parallel to the magnetic field interacts non-linearly with itself, in turn generating E x B zonal flows. Unlike the usual picture of zonal flow drive in which microinstability eigenmodes coherently amplify the flow via modulational instabilities, the self-interaction drive of zonal flows from these eigenmodes are uncorrelated with each other. In the case of ITG driven turbulence, using novel statistical diagnostic methods, it is shown that the associated shearing rate of the fluctuating zonal flows therefore reduces as more toroidal modes are resolved in the simulation. In simulations accounting for the full toroidal domain, such an increase in the density of toroidal modes corresponds in fact to an increase in the system size, leading to a finite system size effect that is distinct from the other better known system size effects such as profile shearing or finite radial extend of the unstable region.
The study of non-adiabatic passing electron dynamics is pursued further to include more reactor relevant conditions such as collisions and background shear flow. It is found that, with increasing collisionality, electrons behave more adiabatic-like, especially the trapped electrons away from MRSs, thereby leading to a decrease in the growth rate of ITG eigenmodes. Furthermore, the shortened electron mean free path in presence of collisions leads to a radial broadening of the fine-structures at the MRS of corresponding eigenmodes. In nonlinear simulations, the turbulent flux levels decrease with increasing collisionality, as a result of the reduced drive from the less unstable ITG eigenmodes. The radial width of the fine structures at MRSs is found to reduce with increasing collisionality as a result of reduced nonlinear modification of the eigenmodes in turbulence simulations. A study of the effect of collisions on the self-interaction mechanism reveals that for physically relevant values of collisionality, the effect of self-interaction is still significant. A preliminary study of the effect of background E x B flow shear shows that the fine-structures associated with the non-adiabatic passing electron response persist even with finite background flow.

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.