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  • 1
    Electronic Resource
    Electronic Resource
    An optimization of beta in the DIII-D tokamak (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 3644-3662 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Accurate equilibrium reconstruction and detailed stability analysis of a strongly shaped, double-null, βT=11% discharge shows that the plasma core is in the second stable regime to ideal ballooning modes. The equilibrium reconstruction using all the available data (coil currents, poloidal magnetic loops, motional Stark effect data, the kinetic pressure profile, the magnetic axis location, and the location of the two q=1 surfaces) shows a region of negative magnetic shear near the magnetic axis, an outer positive shear region, and a low shear region connecting the two. The inner negative shear region allows a large positive shear region near the boundary, even at low q (q95=2.6), permitting a large outer region pressure gradient to be first regime stable. The inner region is in the second stable regime, consistent with the observed axial beta [βT(0)=44%]. In the low shear region p' vanishes, consistent with Mercier stability. This is one way to extend the ballooning limit in shaped plasmas while maintaining stability against external kinks. The n=1 analysis shows that the plasma is unstable to an ideal internal mode, consistent with the experimental observations of a saturated internal m/n=1/1 mode. The core plasma pressure, not being limited by ballooning stability, appears to be reaching a local equilibrium limit at the magnetic axis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.860373
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  • 2
    Electronic Resource
    Electronic Resource
    Optimization of elongated plasma shapes and their current profiles with respect to pressure-driven modes (1989)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 1 (1989), S. 1205-1208 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Optimized equilibria were obtained in three different moderately elongated devices. The plasma cross-sectional shape and current profile were optimized to Mercier and ballooning modes for plasma equilibria in a racetrack device, a V-shaped bean device, and a spherical shell device. The resulting q profiles were nonmonotone. In general, triangulating the plasma increased the Mercier and ballooning stability limits. The spherical shell-shaped equilibrium has inherently favorable Mercier and ballooning stability properties.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858996
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  • 3
    Electronic Resource
    Electronic Resource
    Three-dimensional toroidal equilibria and stability by a variational spectral method (1985)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 28 (1985), S. 869-877 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The characteristics of the partial differential equations describing three-dimensional toroidal magnetohydrodynamic equilibria with nested flux surfaces in inverse flux coordinates are derived and examined. The equilibrium equations are then variationally reduced to a truncated set of ordinary differential equations by decomposing the flux surface geometry into a spectral representation. The magnetic field lines on the flux surfaces are given in terms of a variable stream function to allow optimum choice of the angle coordinates over the flux surfaces and to simplify the treatment in the vicinity of a rational magnetic surface. Analytic properties of the spectral representation and moment equations are considered. Comparative calculations are performed numerically. The results agree well with those calculated using a standard three-dimensional equilibrium code, but the variational spectral method is substantially faster computationally. The Mercier stability criterion is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.865056
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  • 4
    Electronic Resource
    Electronic Resource
    Sensitivity of the kink instability to the pressure profile (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 1724-1734 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The stability of the n=1 ideal kink in DIII-D-like [Fusion Technol. 8, 441 (1985)] configurations is found to depend critically on the details of the current density and pressure profiles. The maximum stable normalized β, βN=β/(I/aB) (I in MA, a in meters, and B0 in tesla), is found to increase dramatically as the peak in the pressure gradient is shifted from the central region toward the plasma boundary. Further, for peaked pressure profiles, the β limit is insensitive to the internal inductance, li, whereas for broad pressure profiles, the β limit depends more strongly on li and can increase with li almost up to the point where the q profile becomes hollow. With broad pressure profiles and a conducting wall at 1.5 minor plasma radii, kink-stable βN values of 5.8−significantly above both the Troyon limit and the ballooning limit−have been found.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.860029
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  • 5
    Electronic Resource
    Electronic Resource
    Higher beta at higher elongation in the DIII-D tokamak (1991)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 2220-2229 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A theoretical and experimental evaluation of axisymmetric stability and axisymmetric control has led to a modification of the vertical position control in the DIII-D tokamak, which now allows operation to within a few percent of the ideal magnetohydrodynamic (MHD) n=0 limit. It is found that the onset the departure from rigid shift behavior in D-shaped plasmas limits plasma elongation to 2.5 in DIII-D. The possibility of avoiding the vertical instability in future tokamaks with highly elongated plasmas is discussed. Recent experiments have focused on utilizing this capability for axisymmetric control to construct plasma shapes optimized to increase the achievable beta. Operation near the axisymmetric stability limit allows an increase in the achieved normalized current Ip/aBT, where Ip is the total plasma current, a is the minor radius, and BT is the toroidal field. Based on stability calculations, an equilibrium was developed to achieve marginal stability simultaneously to axisymmetric, kink, and ballooning instabilities. In the experiment, the shape was altered to higher elongation during the high-beta phase as the current profile broadened. A record high beta for DIII-D of 11% was achieved. The high-beta phase of the discharge lasted 40 msec, approximately one confinement time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.859639
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  • 6
    Electronic Resource
    Electronic Resource
    High-beta discharges in the DIII-D tokamak (1990)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 2 (1990), S. 1280-1286 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Low-q (q95〈3) double-null divertor discharges with values of the volume-average toroidal beta as high as 9.3% have been operated in the DIII-D tokamak [Fusion Technol. 8, 441 (1985)]. In discharges with q95≈5, values of βT/(I/aB) as high as 5 have been obtained. These discharges are shown to be at or below the stability limit to the value of beta for infinite-n, ideal ballooning modes. The discharges are significantly below the beta limit for ideal,low toroidal mode number kink modes. The kink mode beta limit is shown to be strongly dependent on the radial profiles of plasma pressure and current. The theoretical beta limit in DIII-D is shown to be in the range βT/(I/aB)=4 –5 depending on the value of I/aB, and this is consistent with the experiment. High-beta discharges have been operated with ion temperature up to 17 keV. Steady-state, high-beta, low-q operation is demonstrated by a discharge with I/aB=2.6, q95=2.7, in which βT〉7% is maintained for 1.5 sec.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.859543
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  • 7
    Electronic Resource
    Electronic Resource
    Magnetic ripple diffusion and stable INTOR equilibria (1982)
    Springer
    Journal of fusion energy 2 (1982), S. 113-122 
    Details
    ISSN: 1572-9591
    Keywords: ripple transport ; burn control ; fusion reactor ; INTOR
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract Under conditions representative of ignited tokamak operation, ion energy losses are likely to be dominated by transport due to deviation from toroidal field axisymmetry. This asymmetry, termed ripple, induces several distinct physical processes, all of which lead to enhanced ion thermal conduction above the neoclassical value. The net impact of these processes on ignition dynamics is analyzed for an INTOR-like plasma by means of a 1 1/2-D transport code. The radial shift of the plasma to regions of higher ripple during plasma heating results in a substantial broadening of the “window” of values of ripple consistent with favorable ignition and burn characteristics and also provides some measure of automatic burn control. Becauseβ-limiting processes are also prime candidates for burn control, the profiles obtained from the transport analyses are examined for stability with respect to ideal MHD modes. The MHD-limitedβ value increases as the plasma is heated and in fact in the burn phase approaches the value characteristic of a shape-optimized MHD equilibrium. The sensitivity of the transport and MHD results to the choice of plasma density is examined, and it is found that hot-ion mode operation is precluded for devices such as INTOR unless present estimates of both ripple losses andβ-limits are highly pessimistic.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01054578
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