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Energetic Ions in Present-Day Tokamaks
Published in Sergei Sharapov, Energetic Particles in Tokamak Plasmas, 2021
Figure 3.2 illustrates the geometry of ICRH for the on-axis H-minority case (3.10). In a toroidal solenoid, magnetic field at the outer side is lower than that at the inner side, and the radial gradient of the equilibrium magnetic field, B(R) ∼ B0/R makes the cyclotron frequency a function of major radius too. Because the wave with frequency ω propagating from the antenna matches the local cyclotron frequency of H-minority ions, ωBH(R), at some point inside the plasma, the cyclotron resonance ω=ωBH(R) becomes possible at this point. During the resonant interaction between the wave and the H-minority ions, an exchange of energy from the wave to the ions increases mostly perpendicular energy of the ions, which is further delivered to thermal ions and electrons via Coulomb collisions.
Boundary Layer Problem: Acoustic and Tollmienn-Schlichting Waves
Published in Sergey Leble, Anna Perelomova, Dynamical Projectors Method in Hydro and Electrodynamics, 2018
In this chapter, we concentrate our efforts on the mathematical formalism: introducing the complete set of basic modes, we transform the fundamental system of standard conservation laws of fluid mechanics to a set of equivalent equations. In linear approximation, a specific choice of new independent variables splits the system into the set of independent equations for the given modes; the account of nonlinearity naturally introduces the interaction by projecting the fundamental equations set in a vector form. Going to the nonlinear description, we use iterations inside the operator by the small parameter related to amplitude (Mach number for acoustics) and viscosity (Reynolds number). We also analyze the possibilities of the resonant interaction of quasi-plane waves on the level of so-called N-wave systems [15]. Being integrable, such systems admit explicit solutions and plenty of conservation laws. Hence, the detailed investigation of the situation is possible in this approximation.
Photo/Electromagnetic Sources
Published in Peter E. J. Flewitt, Robert K. Wild, Physical Methods for Materials Characterisation, 2017
Peter E. J. Flewitt, Robert K. Wild
Nuclear magnetic resonance (NMR) is a method that considers molecular properties by interrogation of atomic nuclei with magnetic fields and radio frequency (RF) irradiation. The phenomenon arises from the resonant interaction of magnetic moments in a time-invariant magnetic field with the magnetic component of an electromagnetic wave (Abragan 1961, Blumich 2000). The frequency wL of the atomic nuclear response, the Larmor frequency, is related to the strength of the magnetic field, |B1|, at the site of the nucleus by () wL=−γ|B1|=−γB1 where γ is the gyromagnetic ratio.
Resonant growth of inertial oscillations from lee waves in the deep ocean
Published in Geophysical & Astrophysical Fluid Dynamics, 2022
Pierre Labreuche, Chantal Staquet, Julien Le Sommer
The interactions between inertial oscillations (IO) and LW close to the bottom of the ocean and the role of IO in energy dissipation are addressed in the present paper for a range of physical parameters typical of Southern Ocean conditions. Numerical simulations in a vertical plane and resonant interaction theory are combined for this purpose.