High Beta Stability Research Articles

High Performance Beta Titanium Alloys as a New Material Perspective for Cardiovascular Applications

During the last few decades, titanium alloys are more and more popular and developed as biomedical devices because of their excellent biocompatibility, very good combination of mechanical properties and prominent corrosion resistance [1-3]. Recently, a new generation of beta titanium alloys dedicated to biomedical applications has been developed. Based on biocompatible alloying elements such as Ta, Nb, Zr and Mo, these alloys were designed as low modulus alloys [4] or nickel-free superelastic materials [5, 6] mainly for orthopedic or dental applications as osseointegrated implants. Beta type titanium alloys take great advantages from their capacity to display several deformation mechanisms as a function of beta phase stability. Therefore, from low to high beta stability, stress assisted martensitic phase transformation (β-α’’), mechanical twinning or simple dislocation slip can alternatively be observed [7]. As a consequence, a very large range of mechanical properties can be reached, including low apparent modulus, large reversible elastic deformation or high yield stress. Although titanium alloys display now a long history of successful applications in orthopedic and dental devices, none of them have been commercially exploited in the area of coronary stents, despite their superior long term haemocopatibility compared to the 316L stainless steel. However, according to previous researches on the biocompatibility of various metals, the corrosion behavior of stainless steel is dominated by its nickel and chromium components, which may induce redox reaction, hydrolysis and complex metal ion–organic molecule binding reactions, whereas none are observed with titanium [8, 9].

2. How High is the Beta Limit for STs? 2.2: Can Relaxation Events and Stability be Problems?

In order to explore the high-beta attainability of a spherical tokamak, theoretical and simulation researches on the stability and relaxation phenomena problems were reviewed. By classifying various magnetohydrodynamic activities by the impact on the high beta stability, the problems to be solved were identified.

Impact of MHD equilibrium input variations on the high beta stability boundaries of NSTX

Ideal MHD stability limits of anticipated plasma configurations for NSTX [Ono M. et al 2000 Nucl. Fusion 40 557] and the dependence on the parameters defining the MHD equilibrium are evaluated. The study provides a quantitative computational evaluation of the stability limitvariations induced by changes to the equilibrium of NSTX high β plasmas. The analysis is based on a reference free-boundary equilibriumwith β = 41.5%, monotonic safety factor q profile (qa = 12.1, q0 = 2.8) and broad pressure profile p (peaking factor Fp≡p(0)/⟨p⟩ = 1.7). On this reference target local variation of the plasma boundary,and the safety factor q and pressure profiles p are imposed. Localized inflection of the outboard plasma boundary, produced by near field effects from poloidal shaping field coils, weaken the stability due to the destabilization of high n ballooning modes. Variation of the qprofile at different radial locations can also degrade stability. Both experimental profiles from existing tokamaks and spherical torus machines and profiles generated from transportmodelling of anticipated neutral beam heated plasmas are used. Degraded stability is found at increasing pressure peaking factor due to the destabilization of n = 1 kink/ballooning modes. Direct access to the second region of stability is found in certain configurations and, for the entire set ofvariations considered, the lower calculated β limit values are still inthe range of 20.0% without considering the stabilizing effect of thepassive conducting structures.

Stability of high beta tokamak plasmas*

Stability at high beta (the ratio of plasma pressure to magnetic field pressure) is an important requirement for a compact, economically attractive fusion reactor. It is also important in present large tokamak experiments, where the best performance is now often limited by instabilities rather than by energy transport. The past decade has seen major advances in our understanding of the stability of high beta tokamak plasmas, as well as in the achievement of high values of beta. Ideal magnetohydrodynamic (MHD) theory has been remarkably successful in predicting the stability limits, and the scaling of maximum stable beta with the normalized plasma current predicted by Troyon and others has been confirmed in many experiments, yielding a limit βmax≊3.5 (%-m-T/MA) I/aB (where I is the plasma current, a is the minor radius, and B is the toroidal field). The instabilities which are predicted to limit beta have been observed experimentally, in good agreement with theoretical predictions, including long-wavelength kink modes and short-wavelength ballooning instabilities. Advances in understanding of tokamak stability have opened several paths to higher values of beta. The use of strong discharge shaping, approaching the limits of axisymmetric stability, has allowed beta values as high as 12% to be reached in agreement with Troyon scaling. Recent experimental results and ideal MHD modeling have shown that the beta limit depends on the form of the pressure and current density profiles, and modification of the current density to create a centrally peaked profile has allowed beta values up to 6I/aB to be achieved experimentally. Recent experiments have also begun to explore both local and global access to the predicted second stable regime for ballooning modes, with the potential for very high values of β/(I/aB). Preliminary experimental investigations of wall stabilization and radio-frequency (RF) current profile control hold the promise of further improvements in beta through passive and active control of instabilities. The developing understanding of high beta stability and the application of this understanding to present experiments and future fusion devices hold the potential for production of stable, steady state plasmas at high beta with good confinement.

High-beta stability of a toroidal plasma

The high toroidal mode number ideal MHD ballooning mode is shown to stabilize again at large beta, in several sequences of numerical toroidal equilibria. Raising the q profile improves high-beta stability for equilibria with the same poloidal beta and flux surface geometry. A smaller aspect ratio enhances the stabilizing effect of raising the q profile and allows second stability to occur at smaller poloidal beta, though larger total beta.