Simulations of High Harmonic Fast Wave Heating on the C-2U Advanced Beam-Driven Field-Reversed Configuration Device
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EPJ Web of Conferences 157, 03065 (2017) DOI: 10.1051/epjconf/201715703065 22 Topical Conference on Radio-Frequency Power in Plasmas
  Simulations of High Harmonic Fast Wave Heating on the C-2U Advanced Beam-Driven Field-Reversed Configuration Device
Xiaokang Yang1,*, Yuri Petrov2, Francesco Ceccherini1, Alf Koehn3, Laura Galeotti1, Sean Dettrick1, Michl Binderbauer1, and the TAE Team
1Tri Alpha Energy, Inc., P.O. Box 7010, Rancho Santa Margarita, CA 92688, USA 2CompX, P.O. Box 2672, Del Mar, CA 92014, USA
3IGVP, University of Stuttgart, Pfaffenwaldring 31, 70569 Stuttgart, Germany
Abstract. Numerous efforts have been made at Tri-Alpha Energy (TAE) to theoretically explore the physics of microwave electron heating in field-reversed configuration (FRC) plasmas. For the fixed 2D profiles of plasma density and temperature for both electrons and thermal ions and equilibrium field of the C-2U machine, simulations with GENRAY-C ray-tracing code have been conducted for the ratios of  / ci[D] in the range of 6 - 20. Launch angles and antenna radial and axial positions have been optimized in order to simultaneously achieve good wave penetration into the core of FRC plasmas and efficient power damping on electrons. It is found that in an optimal regime, single pass absorption efficiency is 100% and most of the power is deposited inside the separatrix of FRC plasmas, with power damping efficiency of about 72% on electrons and less than 19% on ions. Calculations have clearly demonstrated that substantial power absorption on electrons is mainly attributed to high beta enhancement of magnetic pumping; complete power damping occurs before Landau damping has a significant effect on power absorption.
1 Introduction
high harmonic fast wave (HHFW) heating, which has been successfully adapted to high beta, overdense spherical tokamak (ST) plasmas such as NSTX for the experiments of core electron heating and off-axis current drive [5 - 7].
It is well known that in the regime of fast wave direct electron heating, there are two collisionless damping mechanisms: Landau damping (LD), where the force acting on electrons is FLD = eE//; and transit-time magnetic pumping (TTMP or MP), in which the force is FMP = - //( B//). Here e and   are electron’s charge and magnetic moment, and E// and B// are the parallel components of the fast wave electric and magnetic field, respectively. Conventional fast wave electron heating in tokamak plasmas requires wave parallel phase velocity Vph//    /k//   VTe (electron thermal velocity) for any significant absorption via a dominated LD; MP makes no significant contribution to electron damping and often it can be neglected. Moreover, the absorption of fast wave in tokamak plasmas is weak and therefore it is usually required to have a strong electron preheating by microwaves at electron cyclotron resonant frequency in order to enhance multiple-pass power absorption. However, in high beta, ST plasmas like NSTX, it was found that the MP significantly increases power absorption on electrons over the electron LD alone, and it becomes substantially large at a higher range of phase velocity,  /k//   2.5VTe [5]. The combination of MP and LD can lead to 100% single pass absorption.
The C-2U advanced beam-driven FRC device [1] is a simple compact toroid magnetic confinement system, that is, one without toroidal coils linking the plasma, and thus with predominantly poloidal fields. The attractions of such a configuration for a potential fusion reactor are its very high < e> (near unity) thus allowing for efficient use of magnetic hardware, simple and linear geometry for ease of construction and maintenance, as well as a natural, unrestricted divertor configuration for facilitating energy extraction and fusion ash removal [2].
However, the unique characteristics of C-2U FRC plasmas, for example, the plasma being unusually over- dense ( pe > 30 ce inside the separatrix) and the magnetic field dropping quickly to zero in the plasma core, make it extremely challenging to heat electrons in the core of FRC plasmas. Conventional electron heating scenarios such as electron cyclotron resonant frequency (or its second or third harmonics) heating which is widely utilized in tokamaks, stellarators, and mirror machines, cannot be adapted to FRC plasmas due to the issue of poor wave accessibility into the plasma core. Other electron heating scenarios, such as electron Bernstein waves, upper-hybrid resonant waves, and whistler waves, encounter similar problem or have low heating efficiency when they are applied to FRC plasmas [3, 4]. Fortunately, our recent survey indicated that the conflict between good wave accessibility and efficient power damping on electrons may be solved by using
* Corresponding author: xyang@trialphaenergy.com
 © The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/).






















































































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