Ballooning beta limits of Dee- and bean-shaped tokamaks

Abstract

Numerical studies of the beta limit in the first region of stability for n = °° ballooning modes in advanced-shaped tokamaks are presented. A higher beta value than corresponds to the present conventional beta scaling is expected for advanced-shaped tokamaks with sufficient triangularity/indentation. Extremely elongated configurations without appropriate triangularity do not lead to an increase in critical beta. Dee or bean shapes with sharply tipped cross-sections are more favourable for achieving high beta values than those with round-tip cross-sections having nearly the same safety factor profile. A new beta scaling for elongated ellipse, Dee-and bean-shaped tokamaks is derived.

Aspect Ratio Scaling of Ideal No-wall Stability Limits in High Bootstrap Fraction Tokamak Plasmas

“…For these shape changes, Figure 2b shows that the normalized toroidal beta varies from 3.4 to 5, while the normalized volume-average beta values have only a 5% deviation from a mean value of 3.0 with the exception of the case with the lowest triangularity and highest elongation. These combined results imply that β N is not strictly invariant with respect to large shape variations, as low triangularity apparently degrades β N limits at sufficiently high elongation as was observed previously [38][39][40]. However, β N exhibits significantly less variation as a stability limit parameter than β N when either plasma aspect ratio or boundary shape is varied.…”

Experimental and Theoretical Stability Limits of Highly Elongated Tokamak Plasmas

“…As a consequence, the global energy confinement time also increases since, according to several widely used scaling laws, it is proportional to the plasma current [1]. The second advantage is that vertically elongated and D-shaped cross sections allow much higher b values than circular ones [2][3][4][5][6][7]. b is defined as the ratio of the volume averaged plasma pressure to the magnetic field pressure in vacuum.…”

“…b is defined as the ratio of the volume averaged plasma pressure to the magnetic field pressure in vacuum. The b limit, as determined by ideal magnetohydrodynamic (MHD) stability, has been expressed in a variety of scaling laws [3][4][5][6]. Perhaps the most widely used is the Troyon scaling law [3], b͑%͒ C T I p ͑MA͓͒͞a͑m͒B͑T͔͒, where I p is the plasma current, a is the horizontal minor radius, B is the toroidal magnetic field, and C T is the Troyon factor, which is typically between 2.5 and 4.0, depending on the pressure and current profiles.…”

Stabilization Analysis of Neoclassical Tearing Mode in Fusion Plasmas

“…The time evolution of fusion plasma has been calculated using 1.5-dimensional transport code TOTAL. The plasma equilibrium is solved by Apollo code [3], and the anomalous transport coefficient is obtained using the GLF23 transport model package [4]. This package source program can be downloaded from the web site http:// w3.pppl.gov/ntcc/GLF/.…”