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ABSTRACT: We have combined the methods of probabilistic risk analysis and optimization to devise a technique suitable for the efficient treatment of uncertainties (or the effects of random fluctuations) in the design and analysis of mathematically describable processes. The key step is the approximation, by a multivariable Taylor series expansion, of the influence of random variables on the objective function. Statistical averaging of this expansion leads to a description of the objective function in terms of the moments of the random variables. Knowledge or estimation of these moments allows the optimization to be carried out using standard calculus based techniques. An example is treated with three variations to illustrate the use of this technique for nonlinear sets of equations and objective functions. The method presented here is applicable to process models in manufacturing, systems analysis, and risk analysis.
Risk Analysis 05/2006; 17(1):93 - 96. · 2.37 Impact Factor
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ABSTRACT: The attractiveness of future commercial tokamak reactors is sensitive to the attainable plasma performance, notably plasma energy confinement and allowable beta. The impact of varying levels of confinement and beta on the size and cost of the resulting tokamak reactor is systematically quantified. Several different classes of tokamak reactors are considered, and designs are optimized in terms of cost of electricity (COE) via a coupled physics/engineering/costing systems code. Surprisingly narrow ranges of plasma confinement and beta are found to be simultaneously useful in minimizing the reactor COE, i.e. improvement in only one of these quantities is not useful beyond some point without accompanying improvements in the other. For steady state, current driven reactors characterized by H mode confinement (where τE=HτE,L; τE,L being the confinement time predicted by the ITER.89 L mode scaling, and H ~ 2), the maximum useful Troyon β coefficient (βN) is only ~ 4.3%.mT/MA. These confinement levels are similar to those observed in present day experiments. If slightly better confinement is achievable (i.e. an enhancement factor over L mode of H ~ 2.5), the maximum useful Troyon coefficient increases to βN ~ 6 and the reactor COE decreases by 20%. Inductively driven, pulsed reactors have somewhat increased useful ranges of confinement relative to the steady state cases. In general, increasing the allowable beta over presently accepted limits offers the single biggest improvement in reactor attractiveness of the tokamak concept
Nuclear Fusion 11/2002; 35(5):551. · 4.09 Impact Factor
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ABSTRACT: Longitudinal and transverse impedances have been incorporated into
the ORBIT particle beam dynamics code. This paper deals with
longitudinal impedance calculations. The model has been validated for
low harmonic number ring stability calculations. Successful benchmarking
with the ESME code, for a case without space charge, and with analytical
instability thresholds, for coasting beams with and without space
charge, has been carried out. The model was then applied to the SNS ring
using the measured impedance of the proposed extraction kicker, and it
was found that the instability threshold occurred at about four times
the proposed current for 2 MW operation
Particle Accelerator Conference, 2001. PAC 2001. Proceedings of the 2001; 02/2001
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ABSTRACT: Numerical calculations for the Spallation Neutron Source accumulator ring indicate that lattice resonances excited by the space-charge potential can increase a mismatch significantly by deforming the beam distribution in phase space. Hence increased mismatch leads to enhanced envelope oscillations that are driving the 2:1 parametric resonance leading to halo formation, even for initially matched beams. We have observed this behavior for the 2 nu(x) - 2 nu(y) = 0 resonance and for the 4 nu(y) = 23 resonance. This mechanism for halo formation peculiar to rings through resonance driven mismatch is very sensitive to the tunes, which emphasizes the importance of a careful choice of operating point in tune space.
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 01/2000; 60(6 Pt B):7479-83.
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ABSTRACT: Space-charge-induced emittance growth and halo generation could lead to unacceptably high beam loss in high intensity rings, such as the SNS [1]. In such accelerators, uncontrolled losses to the walls as small as one part in 10 4 would lead to activation, making maintenance difficult. For this reason it is essential to understand the effects of space charge on beam dynamics, and halo generation in particular, in high intensity rings. We have undertaken the study of space charge dynamics in high intensity rings using a particle tracking approach, with self-consistent evaluation of the space charge forces through a particle-in-cell model. Because of the stringent loss requirements, it is necessary to thoroughly guarantee the reliability of these calculations to high precision through comparison with experiments and through convergence studies. In this paper we present the results of convergence studies in the parameters of the model, namely, the number of macroparticles, the resolution...
09/1999;
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ABSTRACT: Uncontrolled beam losses due to space-charge-induced halo
generation are a concern in the accumulator rings of spallation neutron
sources, such as SNS and ESS. Such rings are characterized by high beam
intensities and low uncontrolled beam loss requirements. It is therefore
important to investigate the dynamics of space charge in high intensity
rings. We have done this extensively by using a particle tracking
approach with a self-consistent particle-in-cell code. We have found
that the inclusion of space charge forces is essential in simulating not
only the dynamics of halo generation, but also the formation of the
observed beam profile shapes under typical conditions. Our results
extend the understanding of fundamental space charge physics, which has
been developed for linear accelerators, to rings
Particle Accelerator Conference, 1999. Proceedings of the 1999; 02/1999
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ABSTRACT: Hands-on maintenance of the Spallation Neutron Source (SNS)
Accumulator Ring requires an uncontrolled beam loss of less than 1 nA/m.
A collimator system will be used to obtain this low uncontrolled beam
loss. Some beam dynamics questions related to the collimators have been
studied. Various factors are optimised with the given SNS ring lattice
such as collimating tube length, location, number of collimators,
aperture size of primary collimators and secondary collimators, and
collimator material. The beam dynamics studies indicate that movable
shielding may be necessary for a few hot places downstream of the
primary collimators and also that secondary collimators could be
designed according to their significantly less activation. These
simulations indicate that with proper collimation the uncontrolled beam
loss requirements of the SNS accumulator ring may be achievable
Particle Accelerator Conference, 1999. Proceedings of the 1999; 02/1999
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ABSTRACT: This paper presents the results of calculations of the transverse effects of space charge of coasting beams in rings for three globally comparable lattice configurations: uniform focusing, FODO, and doublet. The parameters of the lattice and the H− beam are chosen similar to those of the SNS accumulator ring. Three models for space charge are considered: 1) a particle core model based on rms beam parameters, 2) a self-consistent particle-in-cell (PIC) model, and 3) a phase-averaged PIC model. In all cases both matched and mismatched K-V distributions are considered by randomly initializing, and then tracking, collections of macroparticles representing the beam. In the particle core model the initial rms values of the macroparticle distributions are used as initial values for solving the envelope equations, including space charge forces and dispersion effects. For matched beams the calculations, performed using a modified version of the injection and tracking code, ACCSIM, reveal only a slight emittance growth and no halo generation with the particle core model. However, the self-consistent PIC model yields greater emittance growth and halo generation, particularly for the doublet lattice in the vertical plane. When the calculations are performed with the phase-averaged particle-in-cell (PIC) model, the results agree substantially with the particle core model, suggesting that the observed self-consistent PIC results are not a consequence of numerical truncation. As further confirmation, we have performed numerical convergence studies using the doublet lattice, and have observed the behavior of the self-consistent PIC model to persist. The tendency for emittance growth and halo generation in the doublet lattice is not surprising, as the fluctuations in beam area, which are an excellent indicator of space charge forces, are larger and more rapid than for the other lattices. For mismatched beams, only the particle core model has been applied at present, and good beam transport is obtained with up to 25% envelope oscillation amplitudes for all three lattices. © 1998 American Institute of Physics.
AIP Conference Proceedings. 11/1998; 448(1):344-358.
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ABSTRACT: Physics and systems design analyses are carried out to estimate
the desired fusion core parameters for an ST based Volume Neutron Source
(ST-VNS) that utilizes a single-turn toroidal field coil (TFC). A design
with a major radius R<sub>0</sub>=1.07 m is estimated to have large
margins in physics, technology, and engineering for the initial
operation at moderate performance (neutron wall load, W<sub>λ
</sub>=0.5-2.0 MW/m<sup>2</sup>). The VNS therefore begins with
technologies already assumed in the ITER EDA, and the relatively
conservative physics to be tested initially by the ST proof-of-principle
experiments presently being built. Given continued advances in
technology via the VNS and in physics via the ST experiments, the design
should permit upgrades to test components and operation at the level of
future Pilot Plant and Power Plants (W<sub>L</sub>=5 MW/m<sup>2</sup>).
This approach to VNS places premium on modular components and remote
maintenance, encourages continued innovation and optimization in ST
fusion and plasma science, and enhances the practicality of the ST
pathway to fusion power
Fusion Engineering, 1997. 17th IEEE/NPSS Symposium; 11/1997
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ABSTRACT: The mechanical design of a spherical torus based volumetric
neutron source (ST VNS) is being studied under the support of a DOE-SBIR
funding. A device capable of staged operation from a neutron wall
loading of 0.5-5.0 MW/m<sup>2</sup> has been scoped out, as the physics
and engineering design assumptions are raised from modest to aggressive
levels. Margins in the design are ensured since operation of the VNS
will be adequate at a wall loading of 2 MW/m<sup>2</sup>. The device has
a naturally diverted plasma with major radius of 1.07 m, a minor radius
of 0.77 m for an aspect ratio of 1.4, an elongation of 3 and
triangularity of 0.6. In the neutral beam driven version, the plasma
current is 11.1 MA and the toroidal field at the plasma major radius is
2.13 T. The baseline fusion power is 151 MW giving an average neutron
wall loading of 2 MW/m<sup>2</sup> on the outboard side over an
accessible area of over 15 m<sup>2</sup> for blanket testing. The device
utilizes a normal Cu conducting bell jar as the return leg of the
toroidal field current, a concept developed at the Oak Ridge National
Laboratory, The current is carried by an unshielded single-turn center
post (CP) made of dispersion strengthened Cu which is cooled by water in
a single pass from top to bottom. A special sliding electrical interface
between the CP and the bed jar is provided on the upper end to allow for
differential expansion and to isolate the CP from tensile and torsional
forces from the bell jar. The ohmic heating in the CP is 153 MW at the
start of operation and increases to 178 MW after 3 full power years of
operation. Over this period the maximum Cu temperature does not exceed
160 C. This report primarily deals with the design of the CP, one of the
most challenging issues of a low aspect ratio spherical torus.
Maintenance approaches for the CP and the divertor assemblies have been
determined and are addressed in the paper
Fusion Engineering, 1997. 17th IEEE/NPSS Symposium; 11/1997
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ABSTRACT: H<sup>-</sup> ion injection into an accumulator ring is a limiting
process for future high-intensity pulsed spallation sources. To
facilitate the injection design process, a method has been developed to
access a tracking code, ACCSIM, from within an optimization package. The
optimization tool is a C++ interactive driver with steepest descent and
genetic algorithm optimization methods and parallel computing
capabilities. Some injection parameters varied in the optimization
process are the H<sup>-</sup> beam size and position, the foil
configuration and thickness, and the horizontal and vertical bump time
profiles. Constraints and figures-of-merit include maximum allowed foil
temperature, maximum allowed space charge tune shifts, maximum allowed
foil traversals, and maximum allowed beam losses. Application of this
method to accumulator ring injection in the proposed National Spallation
Neutron Source (NSNS) is presented
Particle Accelerator Conference, 1997. Proceedings of the 1997; 06/1997
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ABSTRACT: The impact of improvements in plasma confinement and beta on
commercial tokamak embodiments has been systematically investigated.
Cases were investigated for both steady-state and pulsed reactors. A
narrow range of useful confinement enhancement (H factors over the
ITER-89 Power scaling) and Troyon beta limit coefficients g are found to
be beneficial for reducing the cost of electricity (COE). Improvements
in the beta limit (i.e., g) offer the greatest improvement in reactors.
For g limited to about 4, H factors of only 2 are needed. If g of 6 is
attainable, H factors up to 2.5 are useful. Pulsed reactors have
slightly higher useful H factors, ranging from 2.5 for g near 4 to 3 for
g near 6
Fusion Engineering, 1993., 15th IEEE/NPSS Symposium on; 11/1993
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ABSTRACT: The Tokamak Physics Experiment (TPX) has been proposed to
demonstrate steady-state operation and to develop advanced performance
in terms of β and energy confinement. Major TPX cost drivers and
the impact of physics and technology constraints and options on
operating scenarios are identified. Key trade and sensitivity studies
performed using SUPERCODE are summarized
Fusion Engineering, 1993., 15th IEEE/NPSS Symposium on; 11/1993
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ABSTRACT: An analytic parametric scoping tool has been developed for
application to first wall (FW) design problems. Both thermal and
disruption force effects are considered. For the high heat flux and high
disruption load conditions expected in the International Thermonuclear
Experimental Reactor (ITER) device, vanadium alloy and
dispersion-strengthened copper offer the best stress margins using a
somewhat flattened plasma-facing configuration. Ferritic steels also
appear to have an acceptable stress margin, whereas the conventional
stainless steel 316 does not appear feasible. If a full semicircle shape
FW is required, only the vanadium and ferritic steel alloy have
acceptable solutions
Fusion Engineering, 1993., 15th IEEE/NPSS Symposium on; 11/1993
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ABSTRACT: A new code, named SUPERCODE, has been developed to fill the gap between currently available zero dimensional systems codes and highly sophisticated, multidimensional plasma performance codes. The former are comprehensive in content, fast to execute, but rather simple in terms of the accuracy of their physics and engineering models. The latter contain state-of-the-art plasma physics modeling but are limited in engineering content and are time consuming to run. The SUPERCODE upgrades the reliability and accuracy of systems codes by calculating the self consistent 1 1/2-D plasma evolution in a realistic engineering environment. By a combination of variational techniques and careful formulation there is only a modest increase in CPU time over 0-D runs, thereby making the SUPERCODE suitable for use as a systems studies tool. In addition, we have expended considerable effort to make the code user- and programmer friendly, as well as operationally flexible, with the hope of encouraging wide usage throughout the fusion community.
03/1992
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ABSTRACT: Several poloidal field coil design issues are identified when assessing the benefits of high plasma elongaton in an ITER device. Among these are the sensitivity of PF ampere-turens and coil energy to specific constraints on the plasma shape and profiles and the optimal placement of PF coils subject to assumed operating scenarios. Two versons of free boundary equilibrium codes presently under development at the Oak Ridge National Laboratory (ORNL), HEQ and VEQ, are used to solve several PF design problems related to these issues. Recent efforts have been directed toward problems in the analysis of highly elongated, magnetically-limited plasmas, such as X-point and divertor strike-point placement and control. In this report, we describe the capabilities of HEQ and discuss the major options available to the user. Applications of HEQ and VEQ in the area of plasma elongation tradeoff studies are presented. 8 refs., 4 figs., 4 tabs.
12/1987
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ABSTRACT: Analysis of the scrape-off region requires treatment of the plasma transport along and across the field lines and inclusion of the neutral transport effects. A method for modeling the scrape-off region that is presented here uses separate models for each of these aspects that are coupled together through an iteration procedure that requires only minimal numerical effort. The method is applied here to estimate the neutral pumping rates in the pump-limiter and divertor options for a proposed deuterium-tritium (D-T) ignition experiment. High neutral recycling in the vicinity of the neutralizer plate dramatically affects pumping rates for both the pump-limiter and divertor. In both cases, the plasma flow into the channel surrounding the neutralizer plate is greatly reduced by the neutral recycling. The fraction of this flow that is pumped can be large (> 50%), but in general it is dependent on the particular geometry and plasma conditions. It is estimated that pumping speeds approximately greater than 10/sup 5/ L/s are adequate for the exhaust requirements in the pump-limiter and the divertor cases. Also, high neutral recycling on the front surface of the limiter tends to increase the neutral pumping rate.
02/1985;
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ABSTRACT: Neutral pumping rates are calculated for pump-limiter and divertor options of a next step tokamak ignition device using a method that accounts for the coupled effects of neutral transport and plasma transport. For both pump limiters and divertors the plasma flow into the channel surrounding the neutralizer plate is greatly reduced by the neutral recycling. The fraction of this flow that is pumped can be large (>50%) but in general is dependent on the particular geometry and plasma conditions. It is estimated that pumping speeds greater than or approximately 10/sup 5/ L/s are adequate for the exhaust requirements in the pump-limiter and the divertor cases.
12/1984
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ABSTRACT: Plasma transport along divertor field lines was investigated using a two-point model. This treatment requires considerably less effort to find solutions to the transport equations than previously used one-dimensional (1-D) models and is useful for studying general trends. It also can be a valuable tool for benchmarking more sophisticated models. The model was used to investigate the possibility of operating in the so-called high density, low temperature regime.
03/1984;
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ABSTRACT: Initial global scoping studies have been done for small,
steady-state, copper coil, beam-driven tokamaks that are dedicated to
divertor testing. The usual ITER (International Thermonuclear
Experimental Reactor) global physics models (beta limit, energy
confinement, and analytic divertor heat load calculation) are
incorporated, and for performance criteria it is required that the
divertor heat load and plasma collisionality in the edge region be
similar to those expected in ITER. The smallest, lowest-cost devices
satisfying these constraints tend to have major radius below 1 m, plasma
current of 0.5 to 1 MA, low aspect ratio, and costs of a few tens of
millions of dollars. Injection powers of about 4 to 5 MW are needed to
sustain the plasma current, maintain plasma power balance, and provide
the required divertor heat load
Fusion Engineering, 1991. Proceedings., 14th IEEE/NPSS Symposium on;
