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Determination of gross plasma equilibrium from magnetic multipoles

Description: A new approximate technique to determine the gross plasma equilibrium parameters, major radius, minor radius, elongation and triangularity for an up-down symmetric plasma is developed. It is based on a multipole representation of the externally applied poloidal magnetic field, relating specific terms to the equilibrium parameters. The technique shows reasonable agreement with free boundary MHD equilibrium results. The method is useful in dynamic simulation and control studies.
Date: May 1, 1986
Creator: Kessel, C.E.
Partner: UNT Libraries Government Documents Department

Bootstrap current in a tokamak

Description: The bootstrap current in a tokamak is examined by implementing the Hirshman-Sigmar model and comparing the predicted current profiles with those from two popular approximations. The dependences of the bootstrap current profile on the plasma properties are illustrated. The implications for steady state tokamaks are presented through two constraints; the pressure profile must be peaked and {beta}{sub p} must be kept below a critical value.
Date: March 1, 1994
Creator: Kessel, C.E.
Partner: UNT Libraries Government Documents Department

Linear optimal control of tokamak fusion devices

Description: The control of plasma position, shape and current in a tokamak fusion reactor is examined using linear optimal control. These advanced tokamaks are characterized by non up-down symmetric coils and structure, thick structure surrounding the plasma, eddy currents, shaped plasmas, superconducting coils, vertically unstable plasmas, and hybrid function coils providing ohmic heating, vertical field, radial field, and shaping field. Models of the electromagnetic environment in a tokamak are derived and used to construct control gains that are tested in nonlinear simulations with initial perturbations. The issues of applying linear optimal control to advanced tokamaks are addressed, including complex equilibrium control, choice of cost functional weights, the coil voltage limit, discrete control, and order reduction. Results indicate that the linear optimal control is a feasible technique for controlling advanced tokamaks where the more common classical control will be severely strained or will not work. 28 refs., 13 figs.
Date: May 1, 1989
Creator: Kessel, C.E.; Firestone, M.A. & Conn, R.W.
Partner: UNT Libraries Government Documents Department

A simplified model of nuclear heating in tokamaks

Description: The determination of the distribution of heating in fusion devices is important for thermo-mechanical design and analysis. The nuclear heating is a component of the total heating and is the concern of this paper. For toroidal geometries, such as a tokamak, this is difficult to approximate using simple models, and typically requires a two-dimensional neutron-gamma transport calculation. The particular problem is to incorporate the poloidal variation of the heating. A simplified model is developed to approximate the nuclear heating as a function of the poloidal angle and depth into the structure of interest. The technique uses ray-tracing and one-dimensional neutron-gamma transport calculations. This method has great advantage over the multidimensional neutron-gamma transport calculations, particularly for a frequently changing design. The 1.75 m Compact Ignition Tokamak (CIT) design is used as an example, and comparisons with two-dimensional results are given. 8 refs., 17 figs., 2 tabs.
Date: February 1, 1989
Creator: Kessel, C.E.; Liew, S.L. & Ku, L.P.
Partner: UNT Libraries Government Documents Department

Simulation and Analysis of the Hybrid Operating Mode in ITER

Description: The hybrid operating mode in ITER is examined with 0D systems analysis, 1.5D discharge scenario simulations using TSC and TRANSP, and the ideal MHD stability is discussed. The hybrid mode has the potential to provide very long pulses and significant neutron fluence if the physics regime can be produced in ITER. This paper reports progress in establishing the physics basis and engineering limitation for the hybrid mode in ITER.
Date: September 22, 2005
Creator: Kessel, C. E.; Budny, R. V. & Indireshkumar, K.
Partner: UNT Libraries Government Documents Department

Physics Basis and Simulation of Burning Plasma Physics for the Fusion Ignition Research Experiment (FIRE)

Description: The FIRE [Fusion Ignition Research Experiment] design for a burning plasma experiment is described in terms of its physics basis and engineering features. Systems analysis indicates that the device has a wide operating space to accomplish its mission, both for the ELMing H-mode reference and the high bootstrap current/high beta advanced tokamak regimes. Simulations with 1.5D transport codes reported here both confirm and constrain the systems projections. Experimental and theoretical results are used to establish the basis for successful burning plasma experiments in FIRE.
Date: January 18, 2002
Creator: Kessel, C.E.; Meade, D. & Jardin, S.C.
Partner: UNT Libraries Government Documents Department

Advanced Tokamak Scenarios for the FIRE Burning Plasma Experiment

Description: The advanced tokamak (AT) capability of the Fusion Ignition Research Experiment (FIRE) burning plasma experiment is examined with 0-D systems analysis, equilibrium and ideal-MHD stability, radio-frequency current-drive analysis, and full discharge dynamic simulations. These analyses have identified the required parameters for attractive burning advanced tokamak plasmas, and indicate that these are feasible with the present progress on existing experimental tokamaks.
Date: October 12, 2001
Creator: Kessel, C.E.; Ignat, D. & Mau, T.K.
Partner: UNT Libraries Government Documents Department

Plasma Vertical Control with Internal and External Coils in Nest Step Tokamaks

Description: Vertical stability and control are examined for a tokamak configuration intended to be a generic representation of next step devices. Vertical stability calculations show that a critical resistive wall location can be determined for realistic structures, and that the introduction of small amounts of low resistivity material to an all steel structure can significantly reduce the vertical instability growth rate. Vertical control simulations show that internal control coils require significantly less feedback power than external coils, and that low resistivity materials can allow very low feedback powers or coils to be located externally with reasonable feedback powers.
Date: November 3, 2000
Creator: Kessel, C.E.; Heitzenroeder, P. & Jun, C.
Partner: UNT Libraries Government Documents Department

Poloidal Field Design and Plasma Scenarios for FIRE

Description: The FIRE (Fusion Ignition Research Experiment) device is a compact copper magnet experiment to explore driven DT (deuterium-tritium) burning plasma operations. As part of the design study, the poloidal field requirements, self-consistent dynamic discharge evolutions, and the plasma vertical stability and control are examined. Reported here are the PF (poloidal field) coil locations and currents, and a full discharge simulation of the reference configuration. In addition, other configurations are briefly described, and vertical instability growth times and feedback control currents and voltages are given.
Date: October 1, 1999
Creator: Kessel, C.E. & Bulmer, R.H.
Partner: UNT Libraries Government Documents Department

Simulation of DIII-D Flat q Discharges

Description: The Advanced Tokamak plasma configuration has significant potential for the economical production of fusion power. Research on various tokamak experiments are pursuing these plasmas to establish high {beta}, high bootstrap current fraction, 100% noninductive current, and good energy confinement, in a quasi-stationary state. One candidate is the flat q discharge produced in DIII-D, where the safety factor varies from 2.0 on axis, to slightly below 2.0 at the minimum, and then rises to about 3.5 at the 95% surface. This plasma is prototypical of those studied for power plants in the ARIES tokamak studies. The plasma is produced by ramping up the plasma current and ramping down the toroidal field throughout the discharge. The plasma current reaches 1.65 MA, and the toroidal field goes from 2.25 to 1.6 T. The q{sub min} remains high and at large radius, {rho} {approx} 0.6. The plasma establishes an internal transport barrier in the ion channel, and transitions to H-mode. The free-boundary Tokamak Simulation Code (TSC) is being used to model the discharge and project the impact of changes in the plasma current, toroidal field, and injected power programming.
Date: June 25, 2004
Creator: Kessel, C.E.; Garofalo, A. & Terpstra, T.
Partner: UNT Libraries Government Documents Department

Systems Analysis of a Compact Next Step Burning Plasma Experiment

Description: A new burning plasma systems code (BPSC) has been developed for analysis of a next step compact burning plasma experiment with copper-alloy magnet technology. We consider two classes of configurations: Type A, with the toroidal field (TF) coils and ohmic heating (OH) coils unlinked, and Type B, with the TF and OH coils linked. We obtain curves of the minimizing major radius as a function of aspect ratio R(A) for each configuration type for typical parameters. These curves represent, to first order, cost minimizing curves, assuming that device cost is a function of major radius. The Type B curves always lie below the Type A curves for the same physics parameters, indicating that they lead to a more compact design. This follows from that fact that a high fraction of the inner region, r < R-a, contains electrical conductor material. However, the fact that the Type A OH and TF magnets are not linked presents fewer engineering challenges and should lead to a more reliable design. Both the Type A and Type B curves have a minimum in major radius R at a minimizing aspect ratio A typically above 2.8 and at high values of magnetic field B above 10 T. The minimizing A occurs at larger values for longer pulse and higher performance devices. The larger A and higher B design points also have the feature that the ratio of the discharge time to the current redistribution time is largest so that steady-state operation can be more realistically prototyped. A sensitivity study is presented for the baseline Type A configuration showing the dependence of the results on the parameters held fixed for the minimization study.
Date: February 6, 2002
Creator: Jardin, S.C.; Kessel, C.E.; Meade, D. & Neumeyer, C.
Partner: UNT Libraries Government Documents Department

MHD stability regimes for steady state and pulsed reactors

Description: A tokamak reactor will operate at the maximum value of {beta}{equivalent_to}2{mu}{sub 0} < p >/B{sup 2} that is compatible with MHD stability. This value depends upon the plasma current and pressure profiles, the plasma shape and aspect ratio, and the location of nearby conducting structures. In addition, a steady state reactor will minimize its external current drive requirements and thus achieve its maximum economic benefit with a bootstrap fraction near one, I{sub bs}/I{sub p} {approximately} 1, which constrains the product of the inverse aspect ratio and the plasma poloidal beta to be near unity, {epsilon} {beta}{sub p} {approximately} 1. An inductively driven pulsed reactor has different constraints set by the steady-state Ohm`s law which relates the plasma temperature and density profiles to the parallel current density. We present the results obtained during the ARIES I, II/IV, and III and the PULSAR reactor studies where these quantities were optimized subject to different design philosophies. The ARIES-II/IV and ARIES-III designs are both in the second stability regime, but differ in requirements on the form of the profiles at the plasma edge, and in the location of the conducting wall. The relation between these, as well as new attractive MHD regimes not utilized in the ARIES or PULSAR studies is also discussed.
Date: February 1, 1994
Creator: Jardin, S. C.; Kessel, C. E. & Pomphrey, N.
Partner: UNT Libraries Government Documents Department

Ideal MHD Stability of ITER Steady State Scenarios with ITBs

Description: One of ITER goals is to demonstrate feasibility of continuous operations using non-inductive current drive. Two main candidates have been identified for advanced operations: the long duration, high neutron fluency hybrid scenario and the steady state scenario, both operating at a plasma current lower than the reference ELMy scenario [1][2] to minimize the required current drive. The steady state scenario targets plasmas with current 7-10 MA in the flat-top, 50% of which will be provided by the self-generated, pressure-driven bootstrap current. It has been estimated that, in order to obtain a fusion gain Q &gt; 5 at a current of 9 MA, it should be ΒN &gt; 2.5 and H &gt; 1.5 [3]. This implies the presence of an Internal Transport Barrier (ITB). This work discusses how the stability of steady state scenarios with ITBs is affected by the external heating sources and by perturbations of the equilibrium profiles.
Date: July 27, 2011
Creator: Poli, F. M.; Kessel, C. E.; Jardin, S.; Manickam, J.; Chance, M. & Chen, J.
Partner: UNT Libraries Government Documents Department

Development of the ITER Advanced Steady State and Hybrid Scenarios

Description: Full discharge simulations are performed to examine the plasma current rampup, flattop and rampdown phases self-consistently with the poloidal field (PF) coils and their limitations, plasma transport evolution, and heating/current drive (H/CD) sources. Steady state scenarios are found that obtain 100% non-inductive current with Ip = 7.3-10.0 MA, βN ~ 2.5 for H98 = 1.6, Q’s range from 3 to 6, n/nGr = 0.75-1.0, and NB, IC, EC, and LH source have been examined. The scenarios remain within CS/PF coil limits by advancing the pre-magnetization by 40 Wb. Hybrid scenarios have been identified with 35-40% non-inductive current for Ip = 12.5 MA, H98 ~ 1.25, with q(0) reaching 1 at or after the end of rampup. The equilibrium operating space for the hybrid shows a large range of scenarios can be accommodated, and access 925-1300 s flattop burn durations.
Date: September 24, 2010
Creator: Kessel, C. E.; Campbell, D.; Casper, T.; Gribov, Y. & Snipes, J.
Partner: UNT Libraries Government Documents Department

Advanced Tokamak Plasmas in the Fusion Ignition Research Experiment

Description: The Advanced Tokamak (AT) capability of the Fusion Ignition Research Experiment (FIRE) burning plasma experiment is examined with 0-D systems analysis, equilibrium and ideal-MHD stability, radio-frequency current-drive analysis, and full discharge dynamic simulations. These analyses have identified the required parameters for attractive burning AT plasmas, and indicate that these are feasible within the engineering constraints of the device.
Date: October 13, 2003
Creator: Kessel, C.E.; Meade, D.; Swain, D.W.; Titus, P. & Ulrickson, M.A.
Partner: UNT Libraries Government Documents Department

Plasma Profile and Shape Optimization for the Advanced Tokamak Power Plant, ARIES-AT

Description: An advanced tokamak plasma configuration is developed based on equilibrium, ideal-MHD stability, bootstrap current analysis, vertical stability and control, and poloidal-field coil analysis. The plasma boundaries used in the analysis are forced to coincide with the 99% flux surface from the free-boundary equilibrium. Using an accurate bootstrap current model and external current-drive profiles from ray-tracing calculations in combination with optimized pressure profiles, beta(subscript N) values above 7.0 have been obtained. The minimum current drive requirement is found to lie at a lower beta(subscript N) of 5.4. The external kink mode is stabilized by a tungsten shell located at 0.33 times the minor radius and a feedback system. Plasma shape optimization has led to an elongation of 2.2 and triangularity of 0.9 at the separatrix. Vertical stability could be achieved by a combination of tungsten shells located at 0.33 times the minor radius and feedback control coils located behind the shield. The poloidal-field coils were optimized in location and current, providing a maximum coil current of 8.6 MA. These developments have led to a simultaneous reduction in the power plant major radius and toroidal field.
Date: June 5, 2001
Creator: Kessel, C.E.; Mau, T.K.; Jardin, S.C. & Najmabadi, and F.
Partner: UNT Libraries Government Documents Department

Physics Basis for a Spherical Torus Power Plant

Description: The spherical torus, or low-aspect-ratio tokamak, is considered as the basis for a fusion power plant. A special class of wall-stabilized high-beta high-bootstrap fraction low-aspect-ratio tokamak equilibrium are analyzed with respect to MHD stability, bootstrap current and external current drive, poloidal field system requirements, power and particle exhaust and plasma operating regime. Overall systems optimization leads to a choice of aspect ratio A = 1:6, plasma elongation kappa = 3:4, and triangularity delta = 0:64. The design value for the plasma toroidal beta is 50%, corresponding to beta N = 7:4, which is 10% below the ideal stability limit. The bootstrap fraction of 99% greatly alleviates the current drive requirements, which are met by tangential neutral beam injection. The design is such that 45% of the thermal power is radiated in the plasma by Bremsstrahlung and trace Krypton, with Neon in the scrapeoff layer radiating the remainder.
Date: November 1, 1999
Creator: Kessel, C.E.; Menard, J.; Jardin, S.C.; Mau, T.K. & al, et
Partner: UNT Libraries Government Documents Department

MHD stability of tokamak plasmas

Description: This paper will give an overview of the some of the methods which are used to simulate the ideal MHD properties of tokamak plasmas. A great deal of the research in this field is necessarily numerical and the substantial progress made during the past several years has roughly paralleled the continuing availability of more advanced supercomputers. These have become essential to accurately model the complex configurations necessary for achieving MHD stable reactor grade conditions. Appropriate tokamak MHD equilibria will be described. Then the stability properties is discussed in some detail, emphasizing the difficulties of obtaining stable high {beta} discharges in plasmas in which the current is mainly ohmically driven and thus demonstrating the need for tailoring the current and pressure profiles of the plasma away from the ohmic state. The outline of this paper will roughly follow the physics development to attain the second region of stability in the PBX-M device at The Princeton Plasmas Physics Laboratory.
Date: August 1, 1992
Creator: Chance, M. S. Sun, Y. C.; Jardin, S. C.; Kessel, C. E. & Okabayashi, M.
Partner: UNT Libraries Government Documents Department

Long Pulse High Performance Plasma Scenario Development for the National Spherical Torus Experiment

Description: The National Spherical Torus Experiment [Ono et al., Nucl. Fusion, 44, 452 (2004)] is targeting long pulse high performance, noninductive sustained operations at low aspect ratio, and the demonstration of nonsolenoidal startup and current rampup. The modeling of these plasmas provides a framework for experimental planning and identifies the tools to access these regimes. Simulations based on neutral beam injection (NBI)-heated plasmas are made to understand the impact of various modifications and identify the requirements for (1) high elongation and triangularity, (2) density control to optimize the current drive, (3) plasma rotation and/or feedback stabilization to operate above the no-wall limit, and (4) electron Bernstein waves (EBW) for off-axis heating/current drive (H/CD). Integrated scenarios are constructed to provide the transport evolution and H/CD source modeling, supported by rf and stability analyses. Important factors include the energy confinement, Zeff, early heating/H mode, broadening of the NBI-driven current profile, and maintaining q(0) and qmin>1.0. Simulations show that noninductive sustained plasmas can be reached at IP=800 kA, BT=0.5 T, 2.5, N5, 15%, fNI=92%, and q(0)>1.0 with NBI H/CD, density control, and similar global energy confinement to experiments. The noninductive sustained high plasmas can be reached at IP=1.0 MA, BT=0.35 T, 2.5, N9, 43%, fNI=100%, and q(0)>1.5 with NBI H/CD and 3.0 MW of EBW H/CD, density control, and 25% higher global energy confinement than experiments. A scenario for nonsolenoidal plasma current rampup is developed using high harmonic fast wave H/CD in the early low IP and low Te phase, followed by NBI H/CD to continue the current ramp, reaching a maximum of 480 kA after 3.4 s.
Date: January 1, 2006
Creator: Kessel, C.E.; Bell, R.E.; Bell, M.G.; Gates, D.A. & Harvey, R.W.
Partner: UNT Libraries Government Documents Department

The Linear Stability Properties of Medium- to High- n TAEs in ITER

Description: This document provides a detailed report on the successful completion of the DOE OFES Theory Milestone for FY2007: Improve the simulation resolution of linear stability properties of Toroidal Alfvén Eigenmodes (TAE) driven by energetic particles and neutral beams in ITER by increasing the numbers of toroidal modes used to 15.
Date: February 14, 2008
Creator: Gorelenkov, N N; Budny, R V; Kessel, C E; Kramer, G J; McCune, D; Manickam, J et al.
Partner: UNT Libraries Government Documents Department

Ideal MHD Stability Characteristics of Advanced Operating Regimes in Spherical Torus Plasmas and the Role of High Harmonic Fast Waves

Description: The ARIES reactor study group has found an economically attractive ST-based reactor configuration with: A = 1.6, {kappa} = 3.4, {delta} = 0.65, {beta} = 50%, {beta}{sub N} = 7.3, f{sub BS} = 0.95, R{sub 0} = 3.2 meters, B{sub t0} = 2.08 Tesla, and I{sub P} = 28.5 MA which yields a cost of electricity of approximately 80mils/kWh. MHD stability analysis finds that a broad pressure profile is optimal for wall-stabilizing the pressure driven kink modes typical of such configurations, and that wall stabilization is crucial to achieving the high {beta} needed for an economical power plant. The 6MW high-harmonic fast wave system presently being installed on NSTX should allow real-time control of the plasma {beta}, and in combination with NBI may permit experimental investigations of the effect of pressure profile peaking on MHD stability in the near-term. In the longer term, ejection of ions through resonant interaction with HHFW might be used to induce a controllable edge radial electric field with potentially interesting effects on edge MHD and confinement.
Date: June 1, 1999
Creator: Kessel, C.E.; Manickam, J.; Menard, J.E.; Jardin, S.C. & others], S.M. Kaye
Partner: UNT Libraries Government Documents Department

Physics Analysis of the FIRE Experiment

Description: An integrated model of a complete discharge in the FIRE experiment has been developed based on the TSC simulation code. The complete simulation model includes a choice of several models for core transport, combined with an edge pedestal model and the Porcelli sawtooth model. Burn control is provided by feedback on the auxiliary heating power. We find that with the GLF23 and MMM95 transport models, Q &gt;10 operation should be possible for H-mode pedestal temperatures in the range of 4-5 keV.
Date: June 19, 2002
Creator: Jardin, S.C.; Kessel, C.E.; Meade, D.; Breslau, J.; Fu, G.; Gorelenkov, N. et al.
Partner: UNT Libraries Government Documents Department

An algorithm for determining EF coils from fixed-boundary equilibria applied to ARIES III

Description: An algorithm that determines the external EF coils required to produce equilibria calculated by high-resolution, fixed-boundary codes is described. The algorithm permits the specification of the poloidal-field-null location. The EF-coil positions on a specified surface located just outside of the TF coils are optimized to minimize the stored magnetic energy. Results of the application of this algorithm to ARIES-3 are also presented. 7 refs., 2 figs., 2 tabs.
Date: January 1, 1991
Creator: Bathke, C. (Los Alamos National Lab., NM (United States)); Jardin, S.C. & Kessel, C.E. (Princeton Univ., NJ (United States). Plasma Physics Lab.)
Partner: UNT Libraries Government Documents Department

Generation Of High Non-inductive Plasma Current Fraction H-mode Discharges By High-harmonic Last Wave Heating In The National Spherical Torus Experiment

Description: 1.4 MW of 30 MHz high-harmonic fast wave (HHFW) heating, with current drive antenna phasing, has generated a Ip = 300kA, BT (0) = 0.55T deuterium H-mode plasma in the National Spherical Torus Experiment that has a non-inductive plasma current fraction, fNI = 0.7-1. Seventy-five percent of the non-inductive current was generated inside an internal transport barrier that formed at a normalized minor radius, r/a {approx} 0.4 . Three quarters of the non-inductive current was bootstrap current and the remaining non-inductive current was generated directly by HHFW power inside r/a {approx} 0.2.
Date: February 13, 2012
Creator: Taylor, G.; Kessel, C. E.; LeBlanc, B. P.; Mueller, D.; Phillips, D. K.; Valeo, E. J. et al.
Partner: UNT Libraries Government Documents Department