Penetration And Scattering Of Lower Hybrid Waves By Density Fluctuations

Lower Hybrid [LH] ray propagation in toroidal plasma is controlled by a combination of the azimuthal spectrum launched from the antenna, the poloidal variation of the magnetic field, and the scattering of the waves by the density fluctuations. The width of the poloidal and radial RF wave spectrum increases rapidly as the rays penetrate into higher density and scatter from the turbulence. The electron temperature gradient [ETG] spectrum is particularly effective in scattering the LH waves due to its comparable wavelengths and parallel phase velocities. ETG turbulence is also driven by the radial gradient of the electron current density giving rise to an anomalous viscosity spreading the LH-driven plasma currents. The scattered LH spectrum is derived from a Fokker-Planck equation for the distribution of the ray trajectories with a diffusivity proportional to the fluctuations. The LH ray diffusivity is large giving transport in the poloidal and radial wavenumber spectrum in one -or a few passes - of the rays through the core plasma.Institute for Fusion Studie

Orbit-averaged Guiding-center Fokker-Planck Operator

A general orbit-averaged guiding-center Fokker-Planck operator suitable for the numerical analysis of transport processes in axisymmetric magnetized plasmas is presented. The orbit-averaged guiding-center operator describes transport processes in a three-dimensional guiding-center invariant space: the orbit-averaged magnetic-flux invariant \ov{\psi}, the minimum-B pitch-angle coordinate $\xi_{0}$, and the momentum magnitude $p$.Comment: 12 pages, accepted for publication in Physics of Plasma

Kinetic modelling of runaway electron avalanches in tokamak plasmas

Runaway electrons (REs) can be generated in tokamak plasmas if the accelerating force from the toroidal electric field exceeds the collisional drag force due to Coulomb collisions with the background plasma. In ITER, disruptions are expected to generate REs mainly through knock-on collisions, where enough momentum can be transferred from existing runaways to slow electrons to transport the latter beyond a critical momentum, setting off an avalanche of REs. Since knock-on runaways are usually scattered off with a significant perpendicular component of the momentum with respect to the local magnetic field direction, these particles are highly magnetized. Consequently, the momentum dynamics require a full 3-D kinetic description, since these electrons are highly sensitive to the magnetic non-uniformity of a toroidal configuration. A bounce-averaged knock-on source term is derived. The generation of REs from the combined effect of Dreicer mechanism and knock-on collision process is studied with the code LUKE, a solver of the 3-D linearized bounce-averaged relativistic electron Fokker-Planck equation, through the calculation of the response of the electron distribution function to a constant parallel electric field. This work shows that the avalanche effect can be important even in non-disruptive scenarios. RE formation through knock-on collisions is found to be strongly reduced when taking place off the magnetic axis, since trapped electrons cannot contribute to the RE population. The relative importance of the avalanche mechanism is investigated as a function of the key parameters for RE formation; the plasma temperature and the electric field strength. In agreement with theoretical predictions, the simulations show that in low temperature and E-field knock-on collisions are the dominant source of REs and can play a significant role for RE generation, including in non-disruptive scenarios.Comment: 23 pages, 12 figure

Perturbation analysis of trapped-particle dynamics in axisymmetric dipole geometry

The perturbation analysis of the bounce action-angle coordinates $(J,\zeta)$ for charged particles trapped in an axisymmetric dipole magnetic field is presented. First, the lowest-order bounce action-angle coordinates are derived for deeply-trapped particles in the harmonic-oscillator approximation. Next, the Lie-transform perturbation method is used to derive higher-order anharmonic action-angle corrections. Explicit expressions (with anharmonic corrections) for the canonical parallel coordinates $s(J,\zeta)$ and $p_{\|}(J,\zeta)$ are presented, which satisfy the canonical identity $\{s,\; p_{\|}\}(J,\zeta) \equiv 1$. Lastly, analytical expressions for the bounce and drift frequencies (which include anharmonic corrections) yield excellent agreement with exact numerical results.Comment: 16 pages, 3 figure