Fullwave 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 fullwave 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 CMod, demonstrating fully resolved fast and slow LH wave fields using a Maxwellian nonrelativistic plasma dielectric. Significant spectral broadening of the injected wavemore »
 Authors:
 MIT  Plasma Science and Fusion Center Cambridge, MA 02139 (United States)
 Institute fuer Plasma Physik Garching (Germany)
 Computer Science and Mathematics Division, Oak Ridge National Lab Oak Ridge, TN (United States)
 Oak Ridge National Laboratory  Oak Ridge, TN (United States)
 Princeton Plasma Physics Laboratory  Princeton, New Jersey (United States)
 CompX  Del Mar, CA (United States)
 Lodestar Research Corporation  Boulder, CO (United States)
 ATKMission 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), 1113 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. Fullwave 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. Fullwave 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.
"Fullwave Electromagnetic Field Simulations of Lower Hybrid Waves in Tokamaks". United States.
doi:10.1063/1.2098242.
@article{osti_20726328,
title = {Fullwave 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 fullwave 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 CMod, demonstrating fully resolved fast and slow LH wave fields using a Maxwellian nonrelativistic 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 diffractioninduced 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 CMod 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 CMod is 1/10th the scale of ITER requiring 1000 times less computation and simulations of LH in this machine have required on themore »

Full wave simulations of lower hybrid wave propagation in tokamaks
Lower hybrid (LH) waves have the attractive property of damping strongly via electron Landau resonance on relatively fast tail electrons at (2.53)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 wellsuited to driving current in the plasma periphery where the electron temperature is lower, making LH current drive (LHCD) a promising technique for offaxis (r/a{>=}0.60) current profile control in reactor grade plasmas. Established techniques for computing wave propagation and absorption use WKB expansions with nonMaxwellian selfconsistent distributions.In typical plasma conditions with electron densities of several 10{sup 19} m{sup 3} andmore » 
Full wave description of the accessibility of the lowerhybrid resonance to the slow wave in tokamaks
Mode conversion between the fast and slow electromagnetic waves in the lowerhybrid frequency range is considered. This phenomenon determines the accessibility of the lowerhybrid 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 secondorder approximation is used in the mode conversion region leading to Weber's equation from which transmission coefficients are then obtained in various cases. Raytracing results are recovered for a plasma with a linear density profile in a uniform magnetic field. The effect of including a magnetic fieldmore » 
FullWave Studies of Lower Hybrid Wave Propagation in Tokamaks
A fullwave electromagnetic field solver valid the lower hybrid range of frequencies (LHRF) has been developed that utilizes a semispectral 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 wellbehaved electric field solutions for parameters typical of LH current drive experiments in present day sized tokamaks. 
An assessment of full wave effects on the propagation and absorption of lower hybrid waves
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 wellsuited to driving current. Established modeling techniques use WentzelKramersBrillouin (WKB) expansions with selfconsistent nonMaxwellian 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 »