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Title: Full-wave Electromagnetic Field Simulations of Lower Hybrid Waves in Tokamaks

Abstract

The most common method for treating wave propagation in tokamaks in the lower hybrid range of frequencies (LHRF) has been toroidal ray tracing, owing to the short wavelengths (relative to the system size) found in this regime. Although this technique provides an accurate description of 2D and 3D plasma inhomogeneity effects on wave propagation, the approach neglects important effects related to focusing, diffraction, and finite extent of the RF launcher. Also, the method breaks down at plasma cutoffs and caustics. Recent adaptation of full-wave electromagnetic field solvers to massively parallel computers has made it possible to accurately resolve wave phenomena in the LHRF. One such solver, the TORIC code, has been modified to simulate LH waves by implementing boundary conditions appropriate for coupling the fast electromagnetic and the slow electrostatic waves in the LHRF. In this frequency regime the plasma conductivity operator can be formulated in the limits of unmagnetized ions and strongly magnetized electrons, resulting in a relatively simple and explicit form. Simulations have been done for parameters typical of the planned LHRF experiments on Alcator C-Mod, demonstrating fully resolved fast and slow LH wave fields using a Maxwellian non-relativistic plasma dielectric. Significant spectral broadening of the injected wavemore » spectrum and focusing of the wave fields have been found, especially at caustic surfaces. Comparisons with toroidal ray tracing have also been done and differences between the approaches have been found, especially for cases where wave caustics form. The possible role of this diffraction-induced spectral broadening in filling the spectral gap in LH heating and current drive will be discussed.« less

Authors:
;  [1];  [2];  [3]; ; ; ;  [4]; ;  [5];  [6]; ;  [7];  [8]
  1. MIT - Plasma Science and Fusion Center Cambridge, MA 02139 (United States)
  2. Institute fuer Plasma Physik Garching (Germany)
  3. Computer Science and Mathematics Division, Oak Ridge National Lab Oak Ridge, TN (United States)
  4. Oak Ridge National Laboratory -- Oak Ridge, TN (United States)
  5. Princeton Plasma Physics Laboratory - Princeton, New Jersey (United States)
  6. CompX - Del Mar, CA (United States)
  7. Lodestar Research Corporation - Boulder, CO (United States)
  8. ATK-Mission Research Corp. - Newington, VA (United States)
Publication Date:
OSTI Identifier:
20726328
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 787; Journal Issue: 1; Conference: 16. topical conference on radio frequency power in plasmas, Park City, UT (United States), 11-13 Apr 2005; Other Information: DOI: 10.1063/1.2098242; (c) 2005 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ALCATOR DEVICE; BOUNDARY CONDITIONS; COMPARATIVE EVALUATIONS; COUPLING; DIFFRACTION; ELECTRIC CURRENTS; ELECTROMAGNETIC FIELDS; ELECTROMAGNETIC RADIATION; ELECTRONS; LINE BROADENING; LOWER HYBRID CURRENT DRIVE; LOWER HYBRID HEATING; PLASMA SIMULATION; PLASMA WAVES; RELATIVISTIC PLASMA; SURFACES; WAVE PROPAGATION; WAVELENGTHS

Citation Formats

Wright, J.C., Bonoli, P. T., Brambilla, M., D'Azevedo, E., Berry, L.A., Batchelor, D.B., Jaeger, E.F., Carter, M.D., Phillips, C.K., Okuda, H., Harvey, R.W., Myra, J.R., D'Ippolito, D.A., and Smithe, D.N. Full-wave Electromagnetic Field Simulations of Lower Hybrid Waves in Tokamaks. United States: N. p., 2005. Web. doi:10.1063/1.2098242.
Wright, J.C., Bonoli, P. T., Brambilla, M., D'Azevedo, E., Berry, L.A., Batchelor, D.B., Jaeger, E.F., Carter, M.D., Phillips, C.K., Okuda, H., Harvey, R.W., Myra, J.R., D'Ippolito, D.A., & Smithe, D.N. Full-wave Electromagnetic Field Simulations of Lower Hybrid Waves in Tokamaks. United States. doi:10.1063/1.2098242.
Wright, J.C., Bonoli, P. T., Brambilla, M., D'Azevedo, E., Berry, L.A., Batchelor, D.B., Jaeger, E.F., Carter, M.D., Phillips, C.K., Okuda, H., Harvey, R.W., Myra, J.R., D'Ippolito, D.A., and Smithe, D.N. 2005. "Full-wave Electromagnetic Field Simulations of Lower Hybrid Waves in Tokamaks". United States. doi:10.1063/1.2098242.
@article{osti_20726328,
title = {Full-wave Electromagnetic Field Simulations of Lower Hybrid Waves in Tokamaks},
author = {Wright, J.C. and Bonoli, P. T. and Brambilla, M. and D'Azevedo, E. and Berry, L.A. and Batchelor, D.B. and Jaeger, E.F. and Carter, M.D. and Phillips, C.K. and Okuda, H. and Harvey, R.W. and Myra, J.R. and D'Ippolito, D.A. and Smithe, D.N.},
abstractNote = {The most common method for treating wave propagation in tokamaks in the lower hybrid range of frequencies (LHRF) has been toroidal ray tracing, owing to the short wavelengths (relative to the system size) found in this regime. Although this technique provides an accurate description of 2D and 3D plasma inhomogeneity effects on wave propagation, the approach neglects important effects related to focusing, diffraction, and finite extent of the RF launcher. Also, the method breaks down at plasma cutoffs and caustics. Recent adaptation of full-wave electromagnetic field solvers to massively parallel computers has made it possible to accurately resolve wave phenomena in the LHRF. One such solver, the TORIC code, has been modified to simulate LH waves by implementing boundary conditions appropriate for coupling the fast electromagnetic and the slow electrostatic waves in the LHRF. In this frequency regime the plasma conductivity operator can be formulated in the limits of unmagnetized ions and strongly magnetized electrons, resulting in a relatively simple and explicit form. Simulations have been done for parameters typical of the planned LHRF experiments on Alcator C-Mod, demonstrating fully resolved fast and slow LH wave fields using a Maxwellian non-relativistic plasma dielectric. Significant spectral broadening of the injected wave spectrum and focusing of the wave fields have been found, especially at caustic surfaces. Comparisons with toroidal ray tracing have also been done and differences between the approaches have been found, especially for cases where wave caustics form. The possible role of this diffraction-induced spectral broadening in filling the spectral gap in LH heating and current drive will be discussed.},
doi = {10.1063/1.2098242},
journal = {AIP Conference Proceedings},
number = 1,
volume = 787,
place = {United States},
year = 2005,
month = 9
}
  • Alcator C-Mod is similar in density, field, and plasma shape to ITER and consequently, the lower hybrid (LH) wave dispersion is very similar. The differences in temperature between the two devices do affect the relation between n{sub parallel} and the location at which damping occurs. Even with a parallel code, LH on ITER is a petascale problem requiring on the order of 100 000 processor cores and 10 000 poloidal modes to complete in one hour. Alcator C-Mod is 1/10th the scale of ITER requiring 1000 times less computation and simulations of LH in this machine have required on themore » order of 1000 cpu-hours. Therefore, we focus on analysis of full-wave physics effects in LH propagation in Alcator C-Mod using the LH version of the TORIC code [J. C. Wright et al., Phys. Plasmas 11, 2473 (2004)] and contrast those results with ray tracing calculations. Non-Maxwellian effects through development of the quasilinear plateau also play a role and both codes have a generalized dielectric using numerically calculated distributions [Valeo in this proceedings] to incorporate this effect. We will discuss issues of resolution requirements, algorithm improvements, and convergence as well, and speculate on further changes to the algorithms that may enable simulations of ITER with less than petascale requirements.« less
  • Lower hybrid (LH) waves have the attractive property of damping strongly via electron Landau resonance on relatively fast tail electrons at (2.5-3)xv{sub te}, where v{sub te} {identical_to} (2T{sub e}/m{sub e}){sup 1/2} is the electron thermal speed. Consequently these waves are well-suited to driving current in the plasma periphery where the electron temperature is lower, making LH current drive (LHCD) a promising technique for off-axis (r/a{>=}0.60) current profile control in reactor grade plasmas. Established techniques for computing wave propagation and absorption use WKB expansions with non-Maxwellian self-consistent distributions.In typical plasma conditions with electron densities of several 10{sup 19} m{sup -3} andmore » toroidal magnetic fields strengths of 4 Telsa, the perpendicular wavelength is of the order of 1 mm and the parallel wavelength is of the order of 1 cm. Even in a relatively small device such as Alcator C-Mod with a minor radius of 22 cm, the number of wavelengths that must be resolved requires large amounts of computational resources for the full wave treatment. These requirements are met with a massively parallel version of the TORIC full wave code that has been adapted specifically for the simulation of LH waves [J. C. Wright, et al., Commun. Comput. Phys., 4, 545 (2008), J. C. Wright, et al., Phys. Plasmas 16 July (2009)]. This model accurately represents the effects of focusing and diffraction that occur in LH propagation. It is also coupled with a Fokker-Planck solver, CQL3D, to provide self-consistent distribution functions for the plasma dielectric as well as a synthetic hard X-ray (HXR) diagnostic for direct comparisons with experimental measurements of LH waves.The wave solutions from the TORIC-LH zero FLR model will be compared to the results from ray tracing from the GENRAY/CQL3D code via the synthetic HXR diagnostic and power deposition.« less
  • Mode conversion between the fast and slow electromagnetic waves in the lower-hybrid frequency range is considered. This phenomenon determines the accessibility of the lower-hybrid resonance to the slow wave, and is also of theoretical interest because the mode coupling differs in certain aspects from cases previously investigated by the authors and others. A second-order approximation is used in the mode conversion region leading to Weber's equation from which transmission coefficients are then obtained in various cases. Ray-tracing results are recovered for a plasma with a linear density profile in a uniform magnetic field. The effect of including a magnetic fieldmore » gradient is to move the mode conversion region to the plasma edge. The second part of the paper provides justification for the use of Weber's equation. The exact fourth-order system of ordinary differential equations for the problem is set down and a linear transformation, which is an extension of that given by Heading, reveals the second-order nature of the coupling process. Numerical solutions of the fourth-order system yield transmission coefficients in excellent agreement with the second-order theory, and also demonstrate that the electric field variation across the mode conversion region is well approximated, via the above transformation, by the second-order theory.« less
  • A full-wave electromagnetic field solver valid the lower hybrid range of frequencies (LHRF) has been developed that utilizes a semi-spectral representation for the RF electric field. Spurious numerical behavior of the field solver that was found to be related to the inclusion of finite electron Larmor radius terms in the wave equation is discussed. The removal of these terms is shown to eliminate all spurious mode generation, leading to well-behaved electric field solutions for parameters typical of LH current drive experiments in present day sized tokamaks.
  • Lower hybrid (LH) waves ({omega}{sub ci}<<{omega}<<{omega}{sub ce}, where {omega}{sub i,e}{identical_to}Z{sub i,e}eB/m{sub i,e}c) have the attractive property of damping strongly via electron Landau resonance on relatively fast tail electrons and consequently are well-suited to driving current. Established modeling techniques use Wentzel-Kramers-Brillouin (WKB) expansions with self-consistent non-Maxwellian distributions. Higher order WKB expansions have shown some effects on the parallel wave number evolution and consequently on the damping due to diffraction [G. Pereverzev, Nucl. Fusion 32, 1091 (1991)]. A massively parallel version of the TORIC full wave electromagnetic field solver valid in the LH range of frequencies has been developed [J. C. Wrightmore » et al., Comm. Comp. Phys. 4, 545 (2008)] and coupled to an electron Fokker-Planck solver CQL3D[R. W. Harvey and M. G. McCoy, in Proceedings of the IAEA Technical Committee Meeting, Montreal, 1992 (IAEA Institute of Physics Publishing, Vienna, 1993), USDOC/NTIS Document No. DE93002962, pp. 489-526] in order to self-consistently evolve nonthermal electron distributions characteristic of LH current drive (LHCD) experiments in devices such as Alcator C-Mod and ITER (B{sub 0}{approx_equal}5 T, n{sub e0}{approx_equal}1x10{sup 20} m{sup -3}). These simulations represent the first ever self-consistent simulations of LHCD utilizing both a full wave and Fokker-Planck calculation in toroidal geometry.« less