The primary objective of fusion research is to realize a thermonuclear fusion power plant. The main method to confine the hot plasma is by using a magnetic field. The reversed-field pinch is a type of magnetic confinement device which suffers from variety of magnetohy- drodynamic (MHD) instabilities. A particular unstable mode that is treated in this work is the resistive wall mode (RWM), which occurs due to the current gradient in the RFP and has growth rates of the order of the magnetic diffusion time of the wall. Application of control engineering tools appears to allow a robust and stable RFP operation.A model-based approach to stabilize the RWMs is pursued in this thesis. The approach consists of empirical modeling of RWMs using a class of subspace identification methodology. The obtained model is then used as a basis for a model based controller. In particular the first experimental results of using a predictive control for RWM stabilization are obtained. It is shown that the formulation of the model based controller allows the user to incorporate several physics relevant phenomena along with the stabilization of RWM. Another use of the model is shown to estimate and compensate the inherent error field. The results are encouraging, and the methods appear to be generically useful as research tools in controlled magnetic confinement fusion. / Fusionsforskningens primära mål är att förverkliga en ny typ av kraftverk baserade på termonukleär fusion. Den viktigaste metoden för att innesluta det heta plasmat är användandet av  magnetfält. ”Reverserat-fält pinch” (RFP) är en typ av anläggning för magnetisk inneslutning av fusionsplasma som uppvisar ett flertal magneto-hydrodynamiska instabiliteter. En specifik instabil mod som behandlas i detta arbete är”resistiv-vägg” moden (RWM). Den orsakas av strömgradienten i RFPn och tillväxer med en tidskonstant som är av samma storleksordning som magnetfältets diffusionstid i det omgivande metallskalet.  Tillämpning av verktyg från reglerteknikområdet förefaller tillåta en robust och stabil RFP drift. I detta arbete används ett modell-baserat tillvägagångssätt för kompensering av RWM. Det innefattar empirisk modellering av RWM med användning av ”subspace” system-identifieringsmetoder. Den erhållna modellen används sedan som grund för en modell-baserad regulator. De första experimentella resultaten från modell-prediktiv kompensering av RWM har erhållits.  I detta arbete har också visats att formuleringen av den modellbaserade regulatorn tillåter användaren att integrera flera relevanta fysikaliska aspekter förutom RWM. Ytterligare en användning av modellen är för att göra uppskattning och kompensering av avvikelser i anläggningens magnetfält, så kallade fält-fel. Resultaten är uppmuntrande, och det förefaller som om de undersökta metoderna är allmänt användbara som verktyg för forskning om magnetisk inneslutning av fusionsplasma. / <p>QC 20170202</p>

The confinement properties of fusion plasmas are affected bymagnetic and electrostatic fluctuations. The determination ofthe plasma confinement properties requires the measurement ofseveral global and local quantities such as the ion andelectron temperatures, the electron and neutral densityprofiles, the radiation emissivity profiles, the ohmic inputpower and the particle and heat diffusivities. The focus ofthis thesis is the study of the plasma confinement propertiesbased on measurements of these quantities under differentexperimental conditions. The studies have been carried out on the reversed fieldpinch experiments EXTRAP T2 and T2R at the AlfvénLaboratory, Royal Institute of Technology (KTH) in Stockholm.Studies carried out in EXTRAP T2 were focused on dynamoactivity and on the effect of phase alignment and locking tothe wall of magnetic instabilities. These were observed with adedicated imaging system. The experimental studies in EXTRAPT2R were focused on the measurement of the confinementproperties of different configurations. To this aim, a set ofdiagnostics were used some of which were upgraded, such as theinterferometer, while others were newly installed, such as aneutral particle energy analyser and a bolometer array. The dynamo, which is responsible for the plasma sustainment,involves resistive magnetohydrodynamic instabilities thatenhance stochastic transport. Furthermore, the plasmaconfinement properties are in general improved in the presenceof mode rotation. The possibility of reducing the stochastictransport and thereby further improving the confinement hasbeen demonstrated in a current profile control experiment.These results indicate that long pulse operations with aresisitive shell and current profile control are indeedfeasible. KeywordsEXTRAP T2, T2R, reversed field pinch, dynamo,energy confinement time, transport, CCD, bolometer,interferometer, neutral particle energy analyser, PPCD, MonteCarlo / QC 20100524

La dynamique des plasmas de fusion par confinement magnétique dans la configuration Reversed Field Pinch (RFP) est ´étudiée en utilisant la description magnétohydrodynamique (MHD) incompressible. Une méthode pseudo-spectrale et une technique de pénalisation en volume sont utilisées pour résoudre le système d’équations dans un cylindre. Les simulations numériques montrent que la pression joue un rôle important dans la dynamique des RFP et ne peut pas être négligée. Ainsi, ß n’est plus le paramètre principal pour décrire la dynamique des RFPs mais plutôt ß’ ∇, un nouveau paramètre qui équivaut le rapport du module de gradient de pression et le module de la force de Lorentz. A un autre niveau, l’effet du changement de la section poloïdale du RFP sur la dynamique est étudié. Les simulations des écoulements RFP ayant le même nombre de Lundquist et des sections différentes (circulaire et elliptique), montrent une grande différence dans les spectres et la diffusion turbulente radiale. Finalement, les écoulements RFP sont utilisés pour étudier l’effet dynamo. Les résultats obtenus montrent que les écoulements RFP sont capables d’amplifier un champ magnétique passif qui aura une tendance à être plus non-linéaire que le champ magnétique du RFP dans les régimes turbulents. / The dynamics of magnetic fusion plasmas in the Reversed Field Pinch (RFP) configuration are studied using an incompressible magnetohydrodynamics (MHD) description. A pseudospectral method combined with a volume penalization method are used to resolve the governing equations in a straight cylinder. Numerical simulations show that the pressure effects on the RFP dynamics cannot be neglected, and thus the _ parameter is not adequate to characterize the importance of pressure in the dynamics. A new parameter, _0r , which is the ratio of the pressure gradient’s magnitude to the Lorentz force’s magnitude, is proposed to be the proper parameter to describe the RFP dynamics. Another investigated influence on the RFP dynamics is the shaping of the poloidal cross-section. Simulations of flows with the same Lundquist number and different cross-sections (circular and elliptic) show a clear change in the spectral behaviour, as well as in the radial turbulent diffusion. Finally, the RFP flows are used to study the dynamo effect. Numerical results show that RFP flows are capable of amplifying a seed magnetic field, which will have tendency to be more nonlinear than the RFP magnetic field in the turbulent regime.

No description available.

The determination of the plasma confinement propertiesdemand data as the electron temperature, the ionic and electrondensity profiles and the radiative emissivity profiles. Thefocus of this thesis is the importance of radial profiles inspectroscopic diagnostics applied to the EXTRAP-T2Rreversed-field pinch. EXTRAP-T2R is a resistive shell reversed-field pinch with amagnetic field shell penetration time much longer than therelaxation cycle time scale. Significant improvements inconfinement properties derived by quantitative plasmaspectroscopy in the vacuum ultraviolet are observed compared tothe previous device EXTRAP-T2. The low level of magneticturbulence and the good magnetic surfaces in the edge regionexplain this observed improvement. A current profile controlexperiment reduces the stochastic transport, which is connectedto the dynamo, and improves the confinement in EXTRAP-T2R evenmore. A comparison of the electron temperature estimated by usinga ratio of line intensities from the same ionization stage ofoxygen and the Thomson scattering system shows that thedifference is explained by the different spatial dependence ofthe excited state populations and the corresponding emissivityof these spectral lines. A collisional radiative model givesestimates for radial profiles of impurities which are notmeasured in EXTRAP-T2R. The estimated profiles can in turn beused to determine the radial profile of the effective ioncharge, the emissivity and finally the radiative power. Asinput, the model uses radial profiles. Neutral hydrogen is predominantly present in the boundaryregion of the plasma. Spectroscopic investigations in this areashow very asymmetric spectral lines of hydrogen due to themovement of atoms. The velocity of the hydrogen atoms dependson the type of plasma-wall interaction and their measurementhelps to identify the different interaction processes. Theexistence of hydrogen molecules in the edge complicates theinterpretation of the line shapes and on the determination ofthe particle confinement time. <b>Keywords:</b>Reversed-field pinch, EXTRAP-T2R, quantitativeplasma spectroscopy, VUV spectroscopy, line-integrated electrontemperature, oxygen, profiles, confinement properties, powerbalance, hydrogen, particle confinement time.

The Reversed-Field Pinch (RFP) is one of the major alternatives for realizing energy production from thermonuclear fusion. Compared to alternative configurations (such as the tokamak and the stellarator) it has some advantages that suggest that an RFP reactor may be more economic. However, the conventional RFP is flawed with anomalously large energy and particle transport (which leads to unacceptably low energy confinement) due to a phenomenon called the "RFP dynam". The dynamo is driven by the gradient in the plasma current in the plasma core, and it has been shown that flattening of the plasma current profile quenches the dynamo and increases confinement. Various forms of current profile control schemes have been developed and tested in both numerical simulations and experiments. In this thesis an automatic current profile control routine has been developed for the three-dimensional, non-linear resistive magnetohydrodynamic computer code DEBSP. The routine utilizes active feedback of the dynamo associated fluctuating electric field, and is optimized for replacing it with an externally supplied field while maintaining field reversal. By introducing a semi-automatic feedback scheme, the number of free parameters is reduced, making a parameter scan feasible. A scaling study was performed and scaling laws for the confinement of the advanced RFP (an RFP with enhanced confinement due to current profile control) have been obtained. The conclusions from this research project are that energy confinement is enhanced substantially in the advanced RFP and that poloidal beta values are possible beyond the previous theoretical limit beta βΘ &lt; ½. Scalings toward the reactor regime indicate strongly enhanced confinement as compared to conventional RFP scenarios, but the question of reactor viability remains open. / QC 20101101

According to classical linearized resistive magnetohydrodynamics theory, pressuredriven modes are unstable in the reversed-field pinch (RFP) due to unfavorable magnetic field line curvature. The result is based on the assumption of an adiabatic energy equation where anisotropic thermal conduction effects are ignored as compared to convection and compression. In this thesis the effects of heat conduction in the energy equation have been studied. We have examined these effects on the linear stability of pressure-driven resistive modes using boundary value theory (Δ´ ) and a novel initial-value full resistive MHD code employing the Generalized Weighted Residual Method (GWRM). In the Δ´ method, a shooting technique is employed by integrating from the resistive layer to boundaries. The GWRM method, on the other hand, is a time-spectral Galerkin method in which the fully linearized MHD equations are solved. For detailed computations, efficiency requires the temporal and spatial domains to be divided into subdomains. For this purpose, a number of challenging test cases including linearized ideal MHD equations are treated. Numerical and analytical investigations of equilibria reveal that thermal conduction effects are not stabilizing for reactor relevant values of Lundquist number, S0, and normalized pressure, βθ, for tearing-stable plasmas. These studies show that growth rate scales as  γ~_ S0−1/5 , which is weaker than for the adiabatic case, γ~_ S0−1/3. A numerical study of optimized confinement for an advanced RFP scenario including ohmic heating and heat conduction, is also part of this thesis. The fully nonlinear resistive MHD code DEBSP has been employed. We have identified, using both Δ´ and GWRM methods, that the observed crash of the high confinement is caused by resistive, pressure-driven modes. / <p>QC 20130503</p>

No description available.

<p>The determination of the plasma confinement propertiesdemand data as the electron temperature, the ionic and electrondensity profiles and the radiative emissivity profiles. Thefocus of this thesis is the importance of radial profiles inspectroscopic diagnostics applied to the EXTRAP-T2Rreversed-field pinch.</p><p>EXTRAP-T2R is a resistive shell reversed-field pinch with amagnetic field shell penetration time much longer than therelaxation cycle time scale. Significant improvements inconfinement properties derived by quantitative plasmaspectroscopy in the vacuum ultraviolet are observed compared tothe previous device EXTRAP-T2. The low level of magneticturbulence and the good magnetic surfaces in the edge regionexplain this observed improvement. A current profile controlexperiment reduces the stochastic transport, which is connectedto the dynamo, and improves the confinement in EXTRAP-T2R evenmore.</p><p>A comparison of the electron temperature estimated by usinga ratio of line intensities from the same ionization stage ofoxygen and the Thomson scattering system shows that thedifference is explained by the different spatial dependence ofthe excited state populations and the corresponding emissivityof these spectral lines. A collisional radiative model givesestimates for radial profiles of impurities which are notmeasured in EXTRAP-T2R. The estimated profiles can in turn beused to determine the radial profile of the effective ioncharge, the emissivity and finally the radiative power. Asinput, the model uses radial profiles.</p><p>Neutral hydrogen is predominantly present in the boundaryregion of the plasma. Spectroscopic investigations in this areashow very asymmetric spectral lines of hydrogen due to themovement of atoms. The velocity of the hydrogen atoms dependson the type of plasma-wall interaction and their measurementhelps to identify the different interaction processes. Theexistence of hydrogen molecules in the edge complicates theinterpretation of the line shapes and on the determination ofthe particle confinement time.</p><p><b>Keywords:</b>Reversed-field pinch, EXTRAP-T2R, quantitativeplasma spectroscopy, VUV spectroscopy, line-integrated electrontemperature, oxygen, profiles, confinement properties, powerbalance, hydrogen, particle confinement time.</p>

<p>The Reversed-Field Pinch (RFP) is one of the major alternatives for realizing energy production from thermonuclear fusion. Compared to alternative configurations (such as the tokamak and the stellarator) it has some advantages that suggest that an RFP reactor may be more economic. However, the conventional RFP is flawed with anomalously large energy and particle transport (which leads to unacceptably low energy confinement) due to a phenomenon called the "RFP dynam".</p><p>The dynamo is driven by the gradient in the plasma current in the plasma core, and it has been shown that flattening of the plasma current profile quenches the dynamo and increases confinement. Various forms of current profile control schemes have been developed and tested in both numerical simulations and experiments.</p><p>In this thesis an automatic current profile control routine has been developed for the three-dimensional, non-linear resistive magnetohydrodynamic computer code DEBSP. The routine utilizes active feedback of the dynamo associated fluctuating electric field, and is optimized for replacing it with an externally supplied field while maintaining field reversal. By introducing a semi-automatic feedback scheme, the number of free parameters is reduced, making a parameter scan feasible. A scaling study was performed and scaling laws for the confinement of the advanced RFP (an RFP with enhanced confinement due to current profile control) have been obtained.</p><p>The conclusions from this research project are that energy confinement is enhanced substantially in the advanced RFP and that poloidal beta values are possible beyond the previous theoretical limit beta β_Θ < ½. Scalings toward the reactor regime indicate strongly enhanced confinement as compared to conventional RFP scenarios, but the question of reactor viability remains open.</p>