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Representation of Ideal Magnetohydrodynamic Modes

Description: One of the most fundamental properties of ideal magnetohydrodynamics is the condition that plasma motion cannot change magnetic topology. The conventional representation of ideal magnetohydrodynamic modes by perturbing a toroidal equilibrium field through δ Β = ∇ X (xi X B) ensures that δ B • ∇ ψ = 0 at a resonance, with ψ labelling an equilibrium flux surface. Also useful for the analysis of guiding center orbits in a perturbed field is the representation δ Β = ∇ X αB. These two representations are equivalent, but the vanishing of δ B • ∇ψ at a resonance is necessary but not sufficient for the preservation of field line topology, and a indiscriminate use of either perturbation in fact destroys the original equilibrium flux topology. It is necessary to find the perturbed field to all orders in xi to conserve the original topology. The effect of using linearized perturbations on stability and growth rate calculations is discussed
Date: January 15, 2013
Creator: White, Roscoe B.
Partner: UNT Libraries Government Documents Department

Equilibrium Reconstruction on the Large Helical Device

Description: Equilibrium reconstruction is commonly applied to axisymmetric toroidal devices. Recent advances in computational power and equilibrium codes have allowed for reconstructions of three-dimensional fields in stellarators and heliotrons. We present the first reconstructions of finite beta discharges in the Large Helical Device (LHD). The plasma boundary and magnetic axis are constrained by the pressure profile from Thomson scattering. This results in a calculation of plasma beta without a-priori assumptions of the equipartition of energy between species. Saddle loop arrays place additional constraints on the equilibrium. These reconstruction utilize STELLOPT, which calls VMEC. The VMEC equilibrium code assumes good nested flux surfaces. Reconstructed magnetic fields are fed into the PIES code which relaxes this constraint allowing for the examination of the effect of islands and stochastic regions on the magnetic measurements.
Date: July 27, 2012
Creator: Samuel A. Lazerson, D. Gates, D. Monticello, H. Neilson, N. Pomphrey, A. Reiman S. Sakakibara, and Y. Suzuki
Partner: UNT Libraries Government Documents Department

Edge Simulation Laboratory Progress and Plans

Description: The Edge Simulation Laboratory (ESL) is a project to develop a gyrokinetic code for MFE edge plasmas based on continuum (Eulerian) techniques. ESL is a base-program activity of OFES, with an allied algorithm research activity funded by the OASCR base math program. ESL OFES funds directly support about 0.8 FTE of career staff at LLNL, a postdoc and a small fraction of an FTE at GA, and a graduate student at UCSD. In addition the allied OASCR program funds about 1/2 FTE each in the computations directorates at LBNL and LLNL. OFES ESL funding for LLNL and UCSD began in fall 2005, while funding for GA and the math team began about a year ago. ESL's continuum approach is a complement to the PIC-based methods of the CPES Project, and was selected (1) because of concerns about noise issues associated with PIC in the high-density-contrast environment of the edge pedestal, (2) to be able to exploit advanced numerical methods developed for fluid codes, and (3) to build upon the successes of core continuum gyrokinetic codes such as GYRO, GS2 and GENE. The ESL project presently has three components: TEMPEST, a full-f, full-geometry (single-null divertor, or arbitrary-shape closed flux surfaces) code in E, {mu} (energy, magnetic-moment) coordinates; EGK, a simple-geometry rapid-prototype code, presently of; and the math component, which is developing and implementing algorithms for a next-generation code. Progress would be accelerated if we could find funding for a fourth, computer science, component, which would develop software infrastructure, provide user support, and address needs for data handing and analysis. We summarize the status and plans for the three funded activities.
Date: June 5, 2007
Creator: Cohen, R
Partner: UNT Libraries Government Documents Department

The Search for Reconnection and Helicity During Formation of a Bounded Spheromak

Description: Recent results from investigations using insertable magnetic probes at the Sustained Spheromak Physics Experiment (SSPX) [E. B. Hooper et al., Nucl. Fusion 39, 863 (1999)] are presented. Experiments were carried out during pre-programmed, constant amplitude coaxial gun current pulses, where magnetic field increases stepwise with every pulse, but eventually saturates. Magnetic traces from the probe, which is electrically isolated from the plasma and spans the flux conserver radius, indicate there is a time lag at every pulse between the response to the current rise in the open flux surfaces (intercepting the electrodes) and the closed flux surfaces (linked around the open ones). This is interpreted as the time to buildup enough helicity in the open flux surfaces before reconnecting and merging with the closed ones. Future experimental and diagnostic plans to directly estimate the helicity in the open flux surfaces and measure reconnection are briefly discussed.
Date: April 30, 2007
Creator: Romero-Talamas, C A; McLean, H S; Hooper, E B; Wood, R D; LoDestro, L L & Moller, J M
Partner: UNT Libraries Government Documents Department

Magnetic Reconnection in the Spheromak: Physics and Consequences

Description: Magnetic reconnection in the spheromak changes magnetic topology by conversion of injected toroidal flux into poloidal flux and by magnetic surface closure (or opening) in a slowly decaying spheromak. Results from the Sustained Spheromak Physics Experiment, SSPX, are compared with resistive MHD simulations using the NIMROD code. Voltage spikes on the SSPX gun during spheromak formation are interpreted as reconnection across a negative-current layer close to the mean-field x-point. Field lines are chaotic during these events, resulting in rapid electron energy loss to the walls and the low T{sub e} < 50 eV seen in experiment and simulation during strong helicity injection. Closure of flux surfaces (and high T{sub e}) can occur between voltage spikes if they are sufficiently far apart in time; these topology changes are not reflected in the impedance of the axisymmetric gun. Possible future experimental scenarios in SSPX are examined in the presence of the constraints imposed by reconnection physics.
Date: February 28, 2006
Creator: Hooper, E B; Cohen, B I; Hill, D N; LoDestro, L L; McLean, H S; Romero-Talamas, C A et al.
Partner: UNT Libraries Government Documents Department

Geometry Dependence of Stellarator Turbulence

Description: Using the nonlinear gyrokinetic code package GENE/GIST, we study the turbulent transport in a broad family of stellarator designs, to understand the geometry-dependence of the microturbulence. By using a set of flux tubes on a given flux surface, we construct a picture of the 2D structure of the microturbulence over that surface, and relate this to relevant geometric quantities, such as the curvature, local shear, and effective potential in the Schrodinger-like equation governing linear drift modes.
Date: August 10, 2009
Creator: H.E. Mynick, P. Xanthopoulos and A.H. Boozer
Partner: UNT Libraries Government Documents Department

Magnetic Diagnostics for the Lithium Tokamak eXperiment

Description: The Lithium Tokamak eXperiment (LTX) is a spherical tokamak with R0 = 0.4m, a = 0.26m, BTF ∼ 3.4kG, IP ∼ 400kA, and pulse length ∼ 0.25s. The focus of LTX is to investigate the novel, low-recycling Lithium Wall operating regime for magnetically confined plasmas. This regime is reached by placing an in-vessel shell conformal to the plasma last closed flux surface. The shell is heated and then coated with liquid lithium. An extensive array of magnetic diagnostics is available to characterize the experiment, including 80 Mirnov coils (single and double-axis, internal and external to the shell), 34 flux loops, 3 Rogowskii coils, and a diamagnetic loop. Diagnostics are specifically located to account for the presence of a secondary conducting surface and engineered to withstand both high temperatures and incidental contact with liquid lithium. The diagnostic set is therefore fabricated from robust materials with heat and lithium resistance and is designed for electrical isolation from the shell and to provide the data required for highly constrained equilibrium reconstructions.
Date: June 20, 2008
Creator: L. Berzak, R. Kaita, T. Kozub, R. Majeski, and L. Zakharov
Partner: UNT Libraries Government Documents Department

Destruction of Invariant Surfaces and Magnetic Coordinates for Perturbed Magnetic Fields

Description: Straight-field-line coordinates are constructed for nearly integrable magnetic fields. The coordinates are based on the robust, noble-irrational rotational-transform surfaces, whose existence is determined by an application of Greene's residue criterion. A simple method to locate these surfaces is described. Sequences of surfaces with rotational-transform converging to low order rationals maximize the region of straight-field-line coordinates.
Date: November 20, 2003
Creator: Hudson, S.R.
Partner: UNT Libraries Government Documents Department

Theoretical Investigation of Field-Line Quality in a Driven Spheromak

Description: Theoretical studies aimed at predicting and diagnosing field-line quality in a spheromak are described. These include nonlinear 3-D MHD simulations, stability studies, analyses of confinement in spheromaks dominated by either open (stochastic) field lines or approximate flux surfaces, and a theory of fast electrons as a probe of field-line length.
Date: October 7, 2002
Creator: Cohen, R H; Berj, H; Cohen, B I; Fowler, T K; Glasser, A H; Hooper, E B et al.
Partner: UNT Libraries Government Documents Department

Current Density and Plasma Displacement Near Perturbed Rational Surface

Description: The current density in the vicinity of a rational surface of a force-free magnetic field subjected to an ideal perturbation is shown to be the sum of both a smooth and a delta-function distribution, which give comparable currents. The maximum perturbation to the smooth current density is comparable to a typical equilibrium current density and the width of the layer in which the current flows is shown to be proportional to the perturbation amplitude. In the standard linearized theory, the plasma displacement has an unphysical jump across the rational surface, but the full theory gives a continuous displacement.
Date: October 10, 2010
Creator: Boozer, A. H. & Pomphrey, N.
Partner: UNT Libraries Government Documents Department

A "Snowflake" Divertor and its Properties

Description: Handling the power and particle exhaust in fusion reactors based on tokamaks is a challenging problem [1,2]. To bring the energy flux to the divertor plates to an acceptable level (< 10 MW/m2), it is desirable to significantly increase poloidal flux expansion in the divertor area. Some recent ideas include that of a so-called X divertor [3] and a 'snowflake' divertor [4]. We use an acronym SF to designate the latter. In this paper we concentrate on the SF divertor. The general idea behind this configuration is that, by a proper selection of divertor (poloidal field) coils, one can make the null point of the second, not of the first order as in the standard divertor. The separatrix in the vicinity of the X point then acquires a characteristic hexapole structure (Fig. 1), reminiscent of a snowflake, whence the name. The fact that the field has a second-order null, leads to a significant increase of the flux expansion. It was noted in Ref. [4] that the SF configuration is topologically unstable: if the current in the divertor coils is somewhat higher than the one that provides the SF configuration, it becomes a single-null X-point configuration. Conversely, if the coil current becomes somewhat lower, there appear two separate X-points. To solve this problem, one can operate the divertor at the current by roughly 5% higher than the value needed to create the second-order null. Then, configuration becomes robust enough and the shape of the separatrix does not change significantly if the coil current varies by 2-3%. At the same time, the flux expansion still remained by a factor of {approx}3 larger compared to a 'canonical' divertor. Following Ref. [4], we call this configuration a 'SF-plus' configuration. Specific examples in Ref. [4] were given for simple magnetic geometries The aim of this ...
Date: June 21, 2007
Creator: Ryutov, D.
Partner: UNT Libraries Government Documents Department

Measurements and Phenomenological Modeling of Magnetic FluxBuildup in Spheromak Plasmas

Description: Internal magnetic field measurements and high-speed imaging at the Sustained Spheromak Physics Experiment (SSPX) [E. B. Hooper, L. D. Pearlstein, R. H. Bulmer, Nucl. Fusion 39, 863 (1999)] are used to study spheromak formation and field buildup. The measurements are analyzed in the context of a phenomenological model of magnetic helicity based on the topological constraint of minimum helicity in the open flux before reconnecting and linking closed flux. Two stages are analyzed: (1) the initial spheromak formation, i. e. when all flux surfaces are initially open and reconnect to form open and closed flux surfaces, and (2) the stepwise increase of closed flux when operating the gun on a new mode that can apply a train of high-current pulses to the plasma. In the first stage, large kinks in the open flux surfaces are observed in the high-speed images taken shortly after plasma breakdown, and coincide with large magnetic asymmetries recorded in a fixed insertable magnetic probe that spans the flux conserver radius. Closed flux (in the toroidal average sense) appears shortly after this. This stage is also investigated using resistive magnetohydrodynamic simulations. In the second stage, a time lag in response between open and closed flux surfaces after each current pulse is interpreted as the time for the open flux to build helicity, before transferring it through reconnection to the closed flux. Large asymmetries are seen during these events, which then relax to a slowly decaying spheromak before the next pulse.
Date: December 14, 2007
Creator: Romero-Talamas, C A; Hooper, E B; Jayakumar, R; McLean, H S; Wood, R D & Moller, J M
Partner: UNT Libraries Government Documents Department

Pressure-induced Breaking of Equilibrium Flux Surfaces in the W7AS Stellarator

Description: Calculations are presented for two shots in the W7AS stellarator which differ only in the magnitude of the current in the divertor control coil, but have very different values of experimentally attainable β (<β> ≈ 2.7% versus <β> ≈ 1.8%). Equilibrium calculations find that a region of chaotic magnetic field line trajectories fills approximately the outer 1/3 of the cross-section in each of these configurations. The field lines in the stochastic region are calculated to behave as if the flux surfaces are broken only locally near the outer midplane and are preserved elsewhere. The calculated magnetic field line diffusion coefficients in the stochastic regions for the two shots are consistent with the observed differences in the attainable β, and are also consistent with the differences in the reconstructed pressure profiles.
Date: April 24, 2007
Creator: A. Reiman, M.C. Zarnstorff, D. Monticello, A. Weller, J. Geiger, and the W7-AS Team
Partner: UNT Libraries Government Documents Department

The perpendicular electron energy flux driven by magnetic fluctuations in the edge of TEXT-U

Description: A fast bolometer was used for direct measurements of parallel electron energy flux in the edge of TEXT-U. The fluctuating component of the parallel electron energy flux, combined with a measurement of magnetic fluctuations, provides an upper limit to the perpendicular electron flux. This magnetically driven energy flux cannot account for the observed energy flux.
Date: June 12, 1995
Creator: Fiksel, G.; Prager, S.C.; Bengtson, R.D. & Wootton, A.J.
Partner: UNT Libraries Government Documents Department

Physics Considerations in the Design of NCSX

Description: Compact stellarators have the potential to make steady-state, disruption-free magnetic fusion systems with beta approximately 5% and relatively low aspect ratio (R/&lt;a&gt; &lt; 4.5) compared to most drift-optimized stellarators. Magnetic quasi-symmetry can be used to reduce orbit losses. The National Compact Stellarator Experiment (NCSX) is designed to test compact stellarator physics in a high-beta quasi-axisymmetric configuration and to determine the conditions for high-beta disruption-free operation. It is designed around a reference plasma with low ripple, good magnetic surfaces, and stability to the important ideal instabilities at beta approximately 4%. The device size, available heating power, and pulse lengths provide access to a high-beta target plasma state. The NCSX has magnetic flexibility to explore a wide range of equilibrium conditions and has operational flexibility to achieve a wide range of beta and collisionality values. The design provides space to accommodate plasma-facing components for divertor operation and ports for an extensive array of diagnostics.
Date: October 9, 2002
Creator: Neilson, G.H.; Zarnstorff, M.C.; Ku, L.P.; Lazarus, E.A.; Mioduszewski, P.K.; Fenstermacher, M. et al.
Partner: UNT Libraries Government Documents Department

Symmetry breaking at magnetic surfaces and interfaces

Description: Examples represented of how symmetry breaking enters into consideration of the physical properties of magnetic surfaces and ultrathin films. The role of magnetic anisotropy is discussed to understand: (i) the existence of two-dimensional (2D) magnetic long-ranged order at finite temperature, (ii) magnetization scaling behavior at the Curie transition, (iii) the 2D spin reorientation transition, and (iv) step-induced magnetic behavior. Experimental examples cited include ultrathin magnetic Fe and Co overlayer and wedge structures grown onto single crystal substrates that are either flat or curved to produce vicinal surfaces with a continuous gradient in the step density. Also included is an example of an atomically flat manganite intergrowth that appears as a stacking fault in a bulk single crystal of a naturally layered structure.
Date: November 20, 1998
Creator: Qiu, Z. Q.
Partner: UNT Libraries Government Documents Department

Singular surfaces in the open field line region of a diverted tokamak

Description: The structure of the open field lines of a slightly nonaxisymmetric, poloidally diverted tokamak is explored by numerical integration of the field line equations for a simple model field. In practice, the nonaxisymmetry could be produced self-consistently by the nonlinear evolution of a free-boundary MHD mode, or it could be produced by field errors, or it could be imposed externally by design. In the presence of a nonaxisymmetric perturbation, the tokamak is shown to develop open field line regions of differing topology separated by singular surfaces. It is argued that the singular surfaces can be expected to play a role analogous to that of rational toroidal flux surfaces, in terms of constraining ideal MHD perturbations and thus constraining the free-energy that can be tapped by ideal MHD instabilities. The possibility of active control of free-boundary instabilities by means of currents driven on the open singular surfaces, which are directly accessible from the divertor plates, is discussed. Also discussed is the possibility of early detection of imminent disruptions through localized measurement of the singular surface currents.
Date: May 1, 1995
Creator: Reiman, A.
Partner: UNT Libraries Government Documents Department

Edge plasma control by a local island divertor in the Compact Helical System

Description: A local island divertor (LID) experiment was performed on the Compact Helical System (CHS) to demonstrate the principle of the LID. It was clearly demonstrated that the particle flow is controlled by adding a resonant perturbation field to the CHS magnetic configuration, and is guided to the back of an m/n = 1/1 island which is created by the perturbation field. The particles recycled there were pumped out with a pumping rate in the range from a few percent to about 10%. As a result, the line averaged core density was reduced by a factor of about 2 in comparison with non-LID discharges at the same gas puffing rate. In addition to the demonstration of these fundamental divertor functions, a modest improvement of energy confinement was observed, which could be attributed to the edge plasma control by the LID.
Date: December 31, 1997
Creator: Komori, A.; Ohyabu, N. & Masuzaki, S.
Partner: UNT Libraries Government Documents Department

Gyrokinetic Calculations of the Neoclassical Radial Electric Field in Stellarator Plasmas

Description: A novel method to calculate the neoclassical radial electric field in stellarator plasmas is described. The method, which does not have the inconvenience of large statistical fluctuations (noise) of standard Monte Carlo technique, is based on the variation of the combined parallel and perpendicular pressures on a magnetic surface. Using a three-dimensional gyrokinetic delta f code, the calculation of the radial electric field in the National Compact Stellarator Experiment has been carried out. It is shown that a direct evaluation of radial electric field based on a direct calculation of the radial particle flux is not tractable due to the considerable noise.
Date: April 9, 2001
Creator: Lewandowski, J.L.V.; Williams, J.; Boozer, A.H. & Lin, Z.
Partner: UNT Libraries Government Documents Department

Stability and transport in compact quasi-axisymmetric stellarators

Description: The potential performance and flexibility of a compact, quasi-axisymmetric (QAS) stellarator design, has been addressed by studying the effects of varied pressure and rotational transform profiles on the global, ideal magnetohydrodynamic (MHD) stability and the energetic particle transport. The CAS3D and TERPSICHORE code packages were used in the MHD studies while the ORBITMN/ORBIT3D code package was used for the transport simulations of the three field period QAS. To assess robust performance in a medium-size experiment, the VMEC code was used to obtain magnetic flux surfaces for 30 equilibria near the design point, while keeping the boundary shape and the average beta fixed at 3.8%. The plasma equilibria obtained were designated P0X/I0Y as follows: P00/I00 was the baseline configuration. P01, P02 and P03 were defined so that P01 was similar to P00, P02 was more peaked than P01, while P03 was broader than P01. P04 was a very broad, parabolic pressure profile and P05 was the pressure profile used in helias reactor studies based on the W7-X design. The iota profiles were chosen as follows: I01 was linear, maintaining i(0) and i(a) the same as in I00. I02 and I03 were based on I01 and also kept i(0) and i(a) as in the baseline case, but with edge shear increased by a factor of 1.5 and 2. I04 was a linear iota profile with i(0) as for the other profiles, but i(a) higher than 0.5, similar to I01. The pressure and iota profiles are shown in Ref. [2].
Date: July 7, 2000
Creator: Redi, M. H.; Cooper, W. A.; Diallo, A.; Fu, G-Y.; Nuehrenberg, C.; Reiman, A. H. et al.
Partner: UNT Libraries Government Documents Department

Drift waves in general toroidal geometry

Description: A model, based on gyro-kinetic ions and fluid electrons, to study drift waves in low-beta [beta = (kinetic pressure)/(magnetic pressure)] stellarator plasmas is presented. The model equations are written in straight-field-line coordinates and are valid for arbitrary, fully three-dimensional configurations with closed, nested magnetic surfaces. An implicit method, coupled with a subcycling technique for the electrons, is used to solve the time-dependent, along-the-field-line equations. Numerical calculations are carried out for a 3-field-period toroidal heliac. The geometrical effects that enter the model equations are calculated and displayed in physical space using advanced visualization techniques.
Date: February 7, 2000
Creator: Lewandowski, J.L.V.
Partner: UNT Libraries Government Documents Department

Omniclassical Diffusion in Low Aspect Ratio Tokamaks

Description: Recently reported numerical results for axisymmetric devices with low aspect ratio A found radial transport enhanced over the expected neoclassical value by a factor of 2 to 3. In this paper, we provide an explanation for this enhancement. Transport theory in toroidal devices usually assumes large A, and that the ratio B{sub p}/B{sub t} of the poloidal to the toroidal magnetic field is small. These assumptions result in transport which, in the low collision limit, is dominated by banana orbits, giving the largest collisionless excursion of a particle from an initial flux surface. However in a small aspect ratio device one may have B{sub p}/B{sub t} {approx} 1, and the gyroradius may be larger than the banana excursion. Here, we develop an approximate analytic transport theory valid for devices with arbitrary A. For low A, we find that the enhanced transport, referred to as omniclassical, is a combination of neoclassical and properly generalized classical effects, which become dominant in the low-A, B{sub p}/B{sub t} {approx} 1 regime. Good agreement of the analytic theory with numerical simulations is obtained.
Date: March 19, 2004
Creator: Mynick, H. E.; White, R. B. & Gates, D. A.
Partner: UNT Libraries Government Documents Department


Description: Intermittent plasma objects (IPOs) featuring higher pressure than the surrounding plasma, and responsible for {approx}50% of the E x B{sub T} radial transport, are observed in the scrape-off layer (SOL) and edge of the DIII-D tokamak. The skewness of probe and BES intermittent data suggest IPO formation at or near the last closed flux surface (LCFS) and the existence of hole-IPO pairs. The particle content of the IPOs at the LCFS is linearly dependent on the discharge density, however, when normalized to the local averaged density, it is fairly insensitive to density variations. It is also shown that the IPOs thermalize with the background plasma within 1 cm of the LCFS. The IPOs appear in the SOL of both L and H mode discharges carrying {approx}50% of the total SOL radial E x B{sub T} transport at all radii. However, the total flux and the IPO contribution, are highly reduced in H-mode conditions due to the increased confinement.
Date: June 1, 2002
Partner: UNT Libraries Government Documents Department


Description: The power threshold for the L-H transition, P{sub TH}, is low when the ion {del}B drift is toward the X-point and increases significantly when it is away from the X-point. In order to study the cause of this effect, we have compared lower single-null (LSN) discharges with upper single-null (USN) discharges where the ion {del}B drift direction is down in both cases. Since many plasma parameters change with input power, we have made comparisons at the same power level (PTOT=2.3 MW). For these experiments, the LSN discharge is just below PTH (2.7 MW) and the USN discharge is far from P{sub TH} (6.8 MW). We have measured various properties of the edge plasma in an attempt to identify changes that may be responsible for the difference in P{sub TH} for the two cases. The equilibrium flux surfaces and diagnostic measurement locations are shown. The most pronounced difference is the reversal and the increased shear in the poloidal group velocity of the density fluctuations near the plasma edge [1]. These results complement a previous study where the plasma configuration was held fixed and the toroidal field was reversed [2]. In that study, differences in the divertor and X-point plasma were measured. In the present work, the X-point could not be located in the range of the divertor Thomson scattering diagnostic due to top/bottom symmetry issues, and those measurements are not available.
Date: July 1, 2002
Creator: CARLSTROM, T.N.; GROEBNER, R.J.; McKEE, G.R.; MOYER, R.A.; RHODES, T.L.; ROST, J.C. et al.
Partner: UNT Libraries Government Documents Department