Relativistic Fermi-Ulam map: Application to WEGA stellarator lower hybrid power operation

Abstract

Analytical and numerical support is here provided in support of the explanation (H. Laqua et al., submitted to Plasma Physics and Controlled Fusion) for the observation of MeV electrons during Lower Hybrid (LH) operation in EC pre-heated plasma at the WEGA stellarator [M. Otte, H. P. Laqua, E. Chlechowitz, S. Marsen, J. Preinhaelter, T. Stange, A. Rodatos, J. Urban and D. Zhang, Nukleonika, 57 (2012) 171]. In the quoted experiments, LH power from the WEGA TE11 circular waveguide, 9 cm diameter, un-phased, 2.45 GHz antenna, is radiated into a B0.5 T, ne5x10 17 1/m 3 plasma at Te10 eV bulk temperature with an EC-generated 50 keV population of electrons. In response, the fast electrons travel around flux or drift surfaces essentially without collisions, repeatedly interacting with the rf field close to the antenna mouth, and gaining energy in the process. Our WEGA antenna calculations indicate a predominantly standing electric field pattern at the antenna mouth. From a simple approximation of the corresponding Hamiltonian equations of motion we derive here a relativistic generalization of the simplified area-preserving Fermi-Ulam (F-U) map [Lieberman and Lichtenberg, Phys. Rev. A5 (1972) 1852), Lichtenberg, Lieberman, and Cohen, Physica 1D (1980) 291], allowing phase-space global stochasticity analysis. At typical WEGA plasma and antenna conditions, and with correlated phases between electron -antenna electric field interaction events, the F-U map and supporting numerical simulations predict an absolute energy barrier in the range of 300 keV. In contrast, with random phases intervening between interaction events the electron energy can reach ~MeV values, compatible with the measurements on WEGA. underlined the diffusive nature of 2 nd order Fermi processes and developed their kinetic description. Much work has been devoted in the past to relativistic chaos caused by magnetic field perturbations of respectively proton or electron beams in particle accelerators (e.g., Chao et al. 11 ) and free electron lasers (e.g., Chen and Davidson 12 ). In either case, the particles are relativistic to start with, the magnetic field perturbation enters the Hamiltonian via the vector potential, and the beyond a certain interaction parameter threshold the magnetic perturbation acts to scatter particles away from the device axis, where the particle orbits are integrable, thereby deteriorating the device performance. An important non-relativistic variation on the particle chaos caused by magnetic perturbations in accelerators and FELs, are resonant magnetic perturbations 13 deliberately excited at the tokamak edge in order to mitigate the effects of edge localized modes (ELMs). Wave-particle interactions are a special case of a 2 nd order Fermi process; a novel treatment of this particular problem has been recently undertaken by Kominis, Ram and Hizanidis 14 . KeywordsThe present work deals with a special case of 1 st order Fermi acceleration, specifically with electron interacting (or "colliding") with a spatially localized e...

Non-Resonant Microwave Discharge Start-Up in Heliotron J

“…The presence of the observed radiometer signal is explained by synchrotron radiation emitted by high-speed relativistic electrons. Mechanisms of highspeed electron formation are discussed [9,[18][19][20]. A possible mechanism for the formation of high-speed electrons may be the acceleration of electrons in stochastic electric fields [18,20].…”

“…Mechanisms of highspeed electron formation are discussed [9,[18][19][20]. A possible mechanism for the formation of high-speed electrons may be the acceleration of electrons in stochastic electric fields [18,20]. Note that in the presence of fluxes of high-speed electrons in the plasma, the development of instabilities in plasma is possible [21].…”