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Definition of total bootstrap current in tokamaks

Description: Alternative definitions of the total bootstrap current are compared. An analogous comparison is given for the ohmic and auxiliary currents. It is argued that different definitions than those usually employed lead to simpler analyses of tokamak operating scenarios.
Date: June 16, 1995
Creator: Ross, D.W.
Partner: UNT Libraries Government Documents Department

Numerical Calculation of Neoclassical Distribution Functions and Current Profiles in Low Collisionality, Axisymmetric Plasmas

Description: A new code, the Neoclassical Ion-Electron Solver (NIES), has been written to solve for stationary, axisymmetric distribution functions (f ) in the conventional banana regime for both ions and elec trons using a set of drift-kinetic equations (DKEs) with linearized Fokker-Planck-Landau collision operators. Solvability conditions on the DKEs determine the relevant non-adiabatic pieces of f (called h ). We work in a 4D phase space in which Ψ defines a flux surface, θ is the poloidal angle, v is the total velocity referenced to the mean flow velocity, and λ is the dimensionless magnetic moment parameter. We expand h in finite elements in both v and λ#21; . The Rosenbluth potentials, φ#8; and ψ, which define the integral part of the collision operator, are expanded in Legendre series in cos χ , where #31;χ is the pitch angle, Fourier series in cos #18;θ , and finite elements in v . At each ψ , we solve a block tridiagonal system for hi (independent of fe ), then solve another block tridiagonal system for he (dependent on fi ). We demonstrate that such a formulation can be accurately and efficiently solved. NIES is coupled to the MHD equilibrium code JSOLVER [J. DeLucia, et al., J. Comput. Phys. 37 , pp 183-204 (1980).] allowing us to work with realistic magnetic geometries. The bootstrap current is calculated as a simple moment of the distribution function. Results are benchmarked against the Sauter analytic formulas and can be used as a kinetic closure for an MHD code (e.g., M3D-C1 [S.C. Jardin, et al ., Computational Science & Discovery, 4 (2012).]).
Date: June 28, 2012
Creator: B.C. Lyons, S.C. Jardin, and J.J. Ramos
Partner: UNT Libraries Government Documents Department

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

Description: Recent experiments in the low aspect ratio National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40 (2000) 557] have achieved normalized beta values twice the conventional tokamak limit at low internal inductance and with significant bootstrap current. These experimental results have motivated a computational re-examination of the plasma aspect ratio dependence of ideal no-wall magnetohydrodynamic stability limits. These calculations find that the profile-optimized no-wall stability limit in high bootstrap fraction regimes is well described by a nearly aspect ratio invariant normalized beta parameter utilizing the total magnetic field energy density inside the plasma. However, the scaling of normalized beta with internal inductance is found to be strongly aspect ratio dependent at sufficiently low aspect ratio. These calculations and detailed stability analyses of experimental equilibria indicate that the nonrotating plasma no-wall stability limit has been exceeded by as much as 30% in NSTX in a high bootstrap fraction regime.
Date: November 25, 2003
Creator: Menard, J. E.; Bell, M. G.; Bell, R. E.; Gates, D. A.; Kaye, S. M.; LeBlanc, B. P. et al.
Partner: UNT Libraries Government Documents Department

Plasma Physics Regimes in Tokamaks with Li Walls

Description: Low recycling regimes with a plasma limited by a lithium wall surface suggest enhanced stability and energy confinement, both necessary for tokamak reactors. These regimes could make ignition feasible in compact tokamaks. Ignited Spherical Tokamaks (IST), self-sufficient in the bootstrap current, are introduced as a necessary step for development of the physics and technology of power reactors.
Date: August 21, 2003
Creator: Zakharo, L.E.; Gorelenkov, N.N.; White, R.B.; Krasheninnikov, S.I. & Pereverzev, G.V.
Partner: UNT Libraries Government Documents Department

Report for collisional and chaotic transport of energetic particles in toroidal plasma

Description: The authors have made progress in two general areas of confinement plasma physics. (1) We studies a new loss mechanism of the toroidally trapped particles related to the up-down asymmetry of ripple in a tokamak. (2) We estimated the bootstrap current of the particles making transitions between the toroidally and locally states in non-axisymmetric tori, stellarators and tokamaks.
Date: April 1, 1995
Creator: Cary, J.R. & Shasharina, S.G.
Partner: UNT Libraries Government Documents Department

Discharges with high bootstrap current fraction on Tore Supra

Description: Bootstrap current is regarded as a serious candidate for non-inductively driving a significant fraction of the total current. High bootstrap fraction discharges have already been achieved and analysed in several tokamaks, including JT-60, DIII-D and TFTR. Tore Supra (R=2. 36 m, a=0.80 m) is particularly suited for the study of non-inductive discharges and long pulse operation. It is equipped with several of non-inductive current drive/heating systems including Lower Hybrid Current Drive (LHCD), Fast Wave Electron Heating (FWEH), and in the future Electron Cyclotron Heating. Fully non-inductive discharges with enhanced confinement (LHEP mode) have already been obtained in Tore Supra with LHCD. High {Beta}p ({le}1.6) regimes current nave also been achieved in the presence of FWEH. In particular, a discharge with 70% of the total current generated by the bootstrap current was observed. In this context, non-inductive current density profile determination is essential for understanding current drive experiments and ultimately for implementing current profile control. This paper briefly describes two methods developed on Tore Supra to determine the non-inductive current density profiles. The agreement between the two methods has been tested by applying them to ohmic discharges. These methods are then applied to the high bootstrap fraction discharges heated by FWEH. The non-inductive current density profile of these discharges are carried out. and the results are finally compared to several models of bootstrap current including Hirsman`s with low collisionality, matrix formulation and both Kessel and Houlberg matrix formulation.
Date: December 31, 1995
Creator: Joffrin, E.; Saoutic, B.; Basiuk, V.; Forest, C. & Houlberg, W.A.
Partner: UNT Libraries Government Documents Department

Stable bootstrap-current driven equilibria for low aspect ratio tokamaks

Description: Low aspect ratio tokamaks can potentially provide a high ratio of plasma pressure to magnetic pressure {beta} and high plasma current I at a modest size, ultimately leading to a high power density compact fusion power plant. For the concept to be economically feasible, bootstrap current must be a major component of the plasma current. A high value of the Troyon factor {beta}{sub N} and strong shaping are required to allow simultaneous operation at high {beta} and high bootstrap current fraction. Ideal magnetohydrodynamic stability of a range of equilibria at aspect ratio 1.4 is systematically explored by varying the pressure profile and shape. The pressure and current profiles are constrained in such a way as to assure complete bootstrap current alignment. Both {beta}{sub N} and {beta} are defined in terms of the vacuum toroidal field. Equilibria with {beta}{sub N} {ge} 8 and {beta} - 35% to 55% exist which are stable to n = {infinity} ballooning modes, and stable to n = 0, 1,2,3 kink modes with a conducting wall. The dependence of {beta} and {beta}{sub N} with respect to aspect ratio is also considered.
Date: August 1, 1996
Creator: Miller, R.L.; Lin-Liu, Y.R.; Turnbull, A.D.; Chan, V.S.; Pearlstein, L.D.; Sauter, O. et al.
Partner: UNT Libraries Government Documents Department

Bootstrap current close to magnetic axis in tokamaks

Description: It is shown that the bootstrap current density close to the magnetic axis in tokamaks does not vanish in simple electron-ion plasmas because the fraction of the trapped particles is finite. The magnitude of the current density could be comparable to that in the outer core region. This may reduce or even eliminate the need of the seed current.
Date: December 1, 1996
Creator: Shaing, K.C. & Hazeltine, R.D.
Partner: UNT Libraries Government Documents Department


Description: OAK A271 OPTIMUM PLASMA STATES FOR NEXT STEP TOKAMAKS. The dependence of the ideal ballooning {beta} limit on aspect ratio, A, and elongation {kappa} is systematically explored for nearly 100% bootstrap current driven tokamak equilibria in a wide range of the shape parameters (A = 1.2-7.0, {kappa} = 1.5-6.0 with triangularity {delta} = 0.5). The critical {beta}{sub N} is shown to be optimal at {kappa} = 3.0-4.0 for all A studied and increases as A decreases with a dependence close to A{sup -0.5}. The results obtained can be used as a theoretical basis for the choice of optimum aspect ratio and elongation of next step burning plasma tokamaks or tokamak reactors.
Date: November 1, 2002
Partner: UNT Libraries Government Documents Department

DIII-D Advanced Tokamak Research Overview

Description: This paper reviews recent progress in the development of long-pulse, high performance discharges on the DIII-D tokamak. It is highlighted by a discharge achieving simultaneously {beta}{sub N}H of 9, bootstrap current fraction of 0.5, noninductive current fraction of 0.75, and sustained for 16 energy confinement times. The physics challenge has changed in the long-pulse regime. Non-ideal MHD modes are limiting the stability, fast ion driven modes may play a role in fast ion transport which limits the stored energy and plasma edge behavior can affect the global performance. New control tools are being developed to address these issues.
Date: December 1, 1999
Creator: Chan, V.S.; Greenfield, C.M.; Lao, L.L.; Luce, T.C.; Petty, C.C. & Staebler, G.M.
Partner: UNT Libraries Government Documents Department

Time-Scales for Non-Inductive Current Buildup in Low-Aspect-Ratio Toroidal Geometry

Description: The fundamental differences between inductive and non-inductive current buildup are clarified and the associated time-scales and other implications are discussed. A simulation is presented whereby the plasma current in a low-aspect-ratio torus is increased primarily by the self-generated bootstrap current with only 10% coming from external current drive. The maximum obtainable plasma current by this process is shown to scale with the toroidal field strength. The basic physics setting the time-scales can be obtained from a 1D analysis. Comparisons are made between the timescales found here and those reported in the experimental literature.
Date: November 1, 1999
Creator: Jardin, S.C.
Partner: UNT Libraries Government Documents Department

Stability of bootstrap current driven magnetic islands in stellarators

Description: The stability of magnetic island producing perturbations due to fluctuations in the bootstrap current in stellarator configuration is examined. The stability criterion depends on the sign of the derivative of the rotational transform, the pressure gradient and the direction of the equilibrium bootstrap current which is determined by the structure of {parallel}B{parallel}. It is found that quasi-helically symmetric stellarator configurations with p{prime}/{tau}{prime} < 0 are unstable to the formation of bootstrap current driven magnetic islands. The stability of conventional stellarator configurations depends upon the field structure.
Date: March 1, 1994
Creator: Hegna, C.C. & Callen, J.D.
Partner: UNT Libraries Government Documents Department

Investigation of the Spherical Stellarator Concept - Final Report

Description: This document is a final report of the U.S. DOE grant entitled ''Investigation of the Spherical Stellarator Concept'' which supported theoretical and numerical investigation of a novel fusion concept, the ultra-low-aspect-ratio stellarator system called Spherical Stellarator (SS). The research was concentrated on (a) search for principally different types of SS configurations, (b) optimization of SS configurations by varying the parameters of the coil systems, (c) finite beta and finite plasma current (including bootstrap current) equilibria in the SS, and (d) Monte Carlo particle transport simulations for the SS.
Date: October 15, 2000
Creator: Moroz, P.E.
Partner: UNT Libraries Government Documents Department

Calculation of the Non-Inductive Current Profile in High-Performance NSTX Plasmas

Description: The constituents of the current profile have been computed for a wide range of high-performance plasmas in NSTX [M. Ono, et al., Nuclear Fusion 40, 557 (2000)]; these include cases designed to maximize the non-inductive fraction, pulse length, toroidal-β, or stored energy. In the absence of low-frequency MHD activity, good agreement is found between the reconstructed current profile and that predicted by summing the independently calculated inductive, pressure-driven, and neutral beam currents, without the need to invoke any anomalous beam ion diffusion. Exceptions occur, for instance, when there are toroidal Alfven eigenmode avalanches or coupled m/n=1/1+2/1 kink-tearing modes. In these cases, the addition of a spatially and temporally dependent fast ion diffusivity can reduce the core beam current drive, restoring agreement between the reconstructed profile and the summed constituents, as well as bringing better agreement between the simulated and measured neutron emission rate. An upper bound on the fast ion diffusivity of ~0.5-1 m2/sec is found in “MHD-free” discharges, based on the neutron emission, time rate of change of the neutron signal when a neutral beam is stepped, and reconstructed on-axis current density.
Date: February 9, 2011
Creator: Gerhardt, S P; Gates, D; Kaye, S; Menard, J; Bell, M G; Bell, R E et al.
Partner: UNT Libraries Government Documents Department

Progress towards Steady State on NSTX

Description: In order to reduce recirculating power fraction to acceptable levels, the spherical torus concept relies on the simultaneous achievement of high toroidal {beta} and high bootstrap fraction in steady state. In the last year, as a result of plasma control system improvements, the achievable plasma elongation on the National Spherical Torus Experiment (NSTX) has been raised from {kappa} {approx} 2.1 to {kappa} {approx} 2.6--approximately a 25% increase. This increase in elongation has lead to a doubling increase in the toroidal {beta} for long-pulse discharges. The increase in {beta} is associated with an increase in plasma current at nearly fixed poloidal {beta}, which enables higher {beta}{sub t} with nearly constant bootstrap fraction. As a result, for the first time in a spherical torus, a discharge with a plasma current of 1 MA has been sustained for 1 second. Data is presented from NSTX correlating the increase in performance with increased plasma shaping capability. In addition to improved shaping, H-modes induced during the current ramp phase of the plasma discharge have been used to reduce flux consumption during and to delay the onset of MHD instabilities. A modeled integrated scenario, which has 100% non-inductive current drive with very high toroidal {beta}, will also be presented. The NSTX poloidal field coils are currently being modified to produce the plasma shape which is required for this scenario, which requires high triangularity ({delta} {approx} 0.8) at elevated elongation ({kappa} {approx} 2.5). The other main requirement for steady state on NSTX is the ability to drive a fraction of the total plasma current with radio-frequency waves. The results of High Harmonic Fast Wave heating and current drive studies as well as electron Bernstein Wave emission studies will be presented.
Date: January 24, 2005
Creator: Gates, D.A.; Kessel, C.; Menard, J.; Taylor, G.; Wilson, J.R. & co-authors, plus 94
Partner: UNT Libraries Government Documents Department

Bootstrap current in enhanced reversed shear tokamaks for volume neutron source applications

Description: The bootstrap current is evaluated for two reference tokamak designs for a Volume Neutron Source (VNS). One is a larger aspect ratio design using superconducting coils (VNS-SC) and the other is a small aspect ratio design using a solid core with normal conducting toroidal field coils (VNS-ST). The target plasma profiles are taken as representative of the recently observed enhanced reverse shear plasmas with hollow magnetic safety factor (q) profiles in the core and corresponding peaked density profiles. The higher q in the plasma center in combination with peaked density is shown to move the peak in the bootstrap current toward the plasma center. This reduces the current drive requirements to a very small axial seed current and a source localized around the location of the desired minimum in the q profile. Very high bootstrap current fractions can be attained in the VNS-SC design with normalized betas (defined in terms of the vacuum toroidal magnetic field at the geometric center of the plasma) of {beta}{sub N} {le} 3.5. The bootstrap current is lower in the VNS-ST design because of its lower aspect ratio; the highest bootstrap fraction found in these limited cases is 50% at {beta}{sub N} = 5.
Date: December 31, 1995
Creator: Houlberg, W.A.
Partner: UNT Libraries Government Documents Department

Comments on the kinetic dynamo

Description: It is conjectured that transport by parallel mass flow in a braided magnetic field, rather than hyper-resistivity, drives the dynamo effect after stochasticity is established. In this paper the authors do not attempt a rigorous proof of this conjecture, which requires showing that braiding introduces correlations analogous to those giving rise to the neoclassical bootstrap current. The authors do offer plausible arguments for the conjecture and show that it leads to interesting consequences if true. Namely, magnetic fluctuations would then scale with the magnetic Reynolds number S like {tilde B}/B {approximately} S{sup {minus}1/2} and the Rechester-Rosenbluth thermal diffusivity like {chi}e {proportional_to} S{sup {minus}1} . This scaling would explain the highest temperatures obtained in the CTX spheromak. It also suggests that a fully-bootstrapped current drive experiment could be carried out on-the DIII-D tokamak.
Date: August 24, 1995
Creator: Fowler, T.K.
Partner: UNT Libraries Government Documents Department

FWEH Induced High Bootstrap Current on Tore Supra

Description: Bootstrap current is regarded as a good candidate to sustain a large fraction of the plasma current, in the so-called `advanced` regimes of a tokamak reactor. It is thus important to study the stability of such discharges and to control them. By means of fast wave electron heating (FWEH, up to 9.5 MW), stationary high bootstrap discharges (during 5 seconds, Angstrom 40 %) were routinely obtained on Tore Supra. The bootstrap profile is computed with a matrix formulation (1,2) and is directly compared to the calculation of the non-inductive current. The simulation of the loop voltage either with the code CRONOS (1D current diffusion code) using the profile of bootstrap current, or with the knowledge of the resistivity, allows also a self consistent determination of the bootstrap current. First results show that the energy enhancement factor H increases linearly with the fraction of bootstrap current. The bootstrap induced by the FWEH is mainly due to the central pressure electron gradient (the central power deposition strongly peaks the electronic temperature). A 0D study shows that the bootstrap current (I{sub bs}) varies linearly with the poloidal beta (I{sub bs}/I{sub p} = C{sub bs} x {beta}{sub p}). The effect of various plasma parameters (toroidal field B{sub t}, line-integrated density nI, ion and electron temperature, plasma current I{sub p}) on the bootstrap profile, fraction, C{sub bs} and on the confinement are analysed.
Date: January 1, 1997
Creator: Basiuk, V.; Aniel, T.; Becoulet, A.; Hoang, G. T.; Litaudon, X.; Hutter, T. et al.
Partner: UNT Libraries Government Documents Department

Effects of plasma shape and profiles on edge stability in DIII-D

Description: The results of recent experimental and theoretical studies concerning the effects of plasma shape and current and pressure profiles on edge instabilities in DIII-D are presented. Magnetic oscillations with toroidal mode number n {approx} 2--9 and a fast growth time {gamma}{sup {minus}1} = 20--150 {micro}s are often observed prior to the first giant type 1 ELM in discharges with moderate squareness. High n ideal ballooning second stability access encourages edge instabilities by facilitating the buildup of the edge pressure gradient and bootstrap current density which destabilize the intermediate to low n modes. Analysis suggests that discharges with large edge pressure gradient and bootstrap current density are more unstable to n > 1 modes. Calculations and experimental results show that ELM amplitude and frequency can be varied by controlling access to the second ballooning stability regime at the edge through variation of the squareness of the discharge shape. A new method is proposed to control edge instabilities by reducing access to the second ballooning stability regime at the edge using high order local perturbation of the plasma shape in the outboard bad curvature region.
Date: December 1, 1998
Creator: Lao, L.L.; Chan, V.S. & Chen, L.
Partner: UNT Libraries Government Documents Department

Plasma transport near the separatrix of a magnetic island

Description: The simplest non-trivial model of transport across a magnetic island chain in the presence of collisionless streaming along the magnetic field is solved by a Wiener-Hopf procedure. The solution found is valid provided the boundary layers about the island separatrix is narrow compared to the island width. The result demonstrates that when this assumption is satisfied the flattened profile region is reduced by the boundary layer width. The calculation is similar to the recent work by Fitzpatrick but is carried out in the collisionless, rather than the collisional, limit of parallel transport, and determines the plasma parameters on the separatrix self-consistently.
Date: December 1, 1996
Creator: Hazeltine, R.D.; Helander, P. & Catto, P.J.
Partner: UNT Libraries Government Documents Department

Results from D-T experiments on TFTR and implications for achieving an ignited plasma

Description: Progress in the performance of tokamak devices has enable not only the production of significant bursts of fusion energy from deuterium-tritium plasmas in the Tokamak Fusion Test Reactor (TFTR) and the Joint European Torus (JET) but, more importantly, the initial study of the physics of burning magnetically confined plasmas. As a result of the worldwide research on tokamaks, the scientific and technical issues for achieving an ignited plasma are better understood and the remaining questions more clearly defined. The principal research topics which have been studied on TFTR are transport, magnetohydrodynamic stability, and energetic particle confinement. The integration of separate solutions to problems in each of these research areas has also been of major interest. Although significant advances, such as the reduction of turbulent transport by means of internal transport barriers, identification of the theoretically predicted bootstrap current, and the study of the confinement of energetic fusion alpha-particles have been made, interesting and important scientific and technical issues remain. In this paper, the implications for the TFTR experiments for overcoming these remaining issues will be discussed.
Date: July 1, 1998
Creator: Hawryluk, R.J.; Blanchard, W. & Batha, S.
Partner: UNT Libraries Government Documents Department

Recent Progress in MHD Stability Calculations of Compact Stellarators

Description: A key issue for compact stellarators is the stability of beta-limiting MHD modes, such as external kink modes driven by bootstrap current and pressure gradient. We report here recent progress in MHD stability studies for low-aspect-ratio Quasi-Axisymmetric Stellarators (QAS) and Quasi-Omnigeneous Stellarators (QOS). We find that the N = 0 periodicity-preserving vertical mode is significantly more stable in stellarators than in tokamaks because of the externally generated rotational transform. It is shown that both low-n external kink modes and high-n ballooning modes can be stabilized at high beta by appropriate 3D shaping without a conducting wall. The stabilization mechanism for external kink modes in QAS appears to be an enhancement of local magnetic shear due to 3D shaping. The stabilization of ballooning mode in QOS is related to a shortening of the normal curvature connection length.
Date: November 15, 2000
Creator: Fu, G.Y.; Ku, L.P.; Redi, M.H.; Kessel, C.; Monticello, D.A.; Reiman, A. et al.
Partner: UNT Libraries Government Documents Department


Description: Key elements of a sustained advanced tokamak discharge in DIII-D are a large fraction of the total current from bootstrap current (f{sub BS}) and parameters that optimize the capability to use electron cyclotron current drive (ECCD) at {rho} {approx} 0.5 to maintain the desired current profile [1-4]. Increased f{sub BS} results from increasing both the normalized beta ({beta}{sub N}) and the minimum value of the safety factor (q{sub min}). Off-axis ECCD is, for the available gyrotron power, optimized at high {beta}{sub N}, high electron temperature (T{sub e}) and low electron density (n{sub e}). As previously reported [2-4], these required elements have been separately demonstrated: density control at high {beta}{sub N} with n{sub e} {le} 5 x 10{sup 19} m{sup -3} using divertor-region pumping, stability at high {beta}, and off-axis ECCD at the theoretically predicted efficiency. This report summarizes recent work on optimizing and integrating these results through evaluation of the dependence of the beta limit on q{sub min} and q{sub 95}, exploration of discharges with relatively high q{sub min}, testing of feedback control of T{sub e} for control of the q profile evolution, and modification of the current profile time evolution when ECCD is applied.
Date: July 1, 2002
Partner: UNT Libraries Government Documents Department

Resonant Toroidal Alfven Eigenmodes (RTAEs) in Neutral Beam Heated Reverse Magnetic Shear Plasmas on TFTR

Description: Resonant Toroidal Alfven Eigenmodes (RTAEs) [1, 2] excited by neutral beam ions are observed in the region of the internal transport barrier in enhanced reverse shear (ERS) plasmas on TFTR. These modes occur in multiples of the same toroidal mode number in the range n=2-4 and appear as highly localized structures near the minimum in the q-profile with frequency near to that expected for TAEs. Unlike regular TAEs, these modes are observed in plasmas where the birth velocity of beam ions is well below the fundamental or sideband resonance condition. Theoretical analysis indicates that the Toroidicity induced Alfven Eigenmode (TAE) does not exist in these discharges due to strong pressure gradients (of the thermal and fast ions) which moves the mode frequency down into the lower Alfven continuum. However a new non-perturbative analysis (where the energetic particles are allowed to modify the mode frequency and mode structure) indicates that RTAEs can be driven by neutral beam ions in the weak magnetic shear region of ERS plasma, consistent with observations on TFTR. The importance of such modes is that they may affect the alpha particle heating profile or enhance the loss of energetic alpha particles in an advanced tokamak reactor where large internal pressure gradients and reverse magnetic shear operation are required to sustain large bootstrap current.
Date: November 1, 1999
Creator: Cheng, C.Z.; G.Y.-Fu; Gorelenkov, N.N.; Nazikian, R. & Budny, R.V.
Partner: UNT Libraries Government Documents Department