Ricardo Farengo

Monte Carlo simulation of neutral beam injection into a field reversed configuration

A Monte Carlo code is employed to study the interaction of neutral beams with a field reversed configuration (FRC). The code follows the exact particle trajectories in the self-consistent equilibrium calculated including the beam and plasma currents. For high enough beam currents, a self-consistent confining effect is observed which prevents expansion of the beam along the FRC axis. The beam current drive and the power and momentum transferred are calculated for a variety of beam parameters. The results are slightly affected by the details of the injection geometry. The dependence on the neutral current IN and beam energy EN is influenced by several factors, such as particle losses through the ends, the density increase around the injection region and the finite Larmor radius effect.

Alpha particle redistribution due to experimentally reconstructed internal kink modes

The redistribution of alpha particles due to internal kink modes is calculated. The exact particle trajectories in the total, equilibrium plus perturbation, fields are calculated. The equilibrium magnetic field is obtained by analytically solving the Grad–Shafranov equation. The perturbed electric and magnetic fields are reconstructed using the experimental information about the displacement eigenfunction. An effective diffusion coefficient is introduced to quantify the magnitude of the particle redistribution produced by the perturbations.

Relaxation of spheromak configurations with open flux

The relaxation of several kink unstable equilibria with open flux representative of spheromaks sustained by dc helicity injection is studied by means of three-dimensional, resistive magnetohydrodynamic simulations. No external driving is applied, but the initial conditions are chosen to reproduce the current profiles existing in a gun driven spheromak, which has a high current density in the open flux region and a low current density in the closed flux region. The growth and nonlinear saturation of various unstable modes, the dynamo action which converts toroidal flux into poloidal flux, and the evolution of the λ profile (λ=μ0J⋅B/B2) are studied. An initial condition is found which results in a dynamo that produces enough poloidal flux to compensate the resistive losses occurred during a characteristic time of the instability. The flux amplification factor around which this case oscillates is consistent with existing experimental data. During the relaxation, the central open flux tube develops a helical ...

Relaxed, minimum dissipation states, for a flux core spheromak sustained by helicity injection

Minimum dissipation states of a flux core spheromak sustained by helicity injection are presented. Helicity balance is used as a constraint and the resistivity is considered to be non-uniform. Two types of relaxed states are found: one has a central core formed by the flux that links the electrodes surrounded by a toroidal region of closed flux surfaces and the other has the open flux wrapped around the closed flux surfaces. The analysis includes two important features: a self-consistent calculation of the magnetic flux through the electrodes and a resistivity which depends upon the poloidal flux. Non-uniform resistivity effects can be very important because of the qualitative and quantitative changes they produce in the safety factor profile.

Development of magnetohydrodynamic modes during sawteeth in tokamak plasmas

A dynamical analysis applied to a reduced resistive magnetohydrodynamics model is shown to explain the chronology of the nonlinear destabilization of modes observed in tokamak sawteeth. A special emphasis is put on the nonlinear self-consistent perturbation of the axisymmetric m = n = 0 mode that manifests through the q-profile evolution. For the very low fusion-relevant resistivity values, the q-profile is shown to remain almost unchanged on the early nonlinear timescale within the central tokamak region, which supports a partial reconnection scenario. Within the resistive region, indications for a local flattening or even a local reversed-shear of the q-profile are given. The impact of this ingredient in the occurrence of the sawtooth crash is discussed.

Nonlinear dynamics of kink-unstable spheromak equilibria

The nonlinear evolution of several kink-unstable, force-free equilibria inside a cylindrical flux conserver is studied by solving the nonlinear, three-dimensional, time-dependent equations of resistive magnetohydrodynamics (MHD). The stability properties of the equilibria are controlled by the slope, α, of the linear λ(ψ) profile (where λ=μ0J⋅B/B2 and ψ is the poloidal flux). Very unstable configurations (with α well beyond the stability threshold) are observed to fully relax toward the Taylor state, as predicted by relaxation theory. In contrast, marginally unstable cases undergo only partial relaxation. Since we consider decaying plasmas without open flux (no driving), the partial relaxation process is a result of the dynamics of marginally unstable configurations. The effect of the Lundquist number, S, on a fixed initial condition (a fixed α) is studied. Increasing S leads to a higher level of fluctuations and poloidal flux amplification. However, it is found that, despite the stronger activity, the fi...

Rotating magnetic field current drive in a hollow plasma column with a steady toroidal field

The effect of a steady azimuthal magnetic field on rotating magnetic field current drive is studied. The configuration considered consists of an infinitely long plasma column with a finite radius conductor, which carries a steady longitudinal current, running along its axis. The ions are assumed to be fixed and the electrons are described using an Ohm’s law that contains the Hall term. A fully two-dimensional computer code is developed to solve the resulting time-dependent equations. For some values of the steady azimuthal field, two steady-state solutions with different efficiencies are found.

Ionization, stopping, and thermalization of hydrogen and boron beams injected in fusion plasmas

The ionization, stopping, and thermalization of hydrogen and boron beams, injected, respectively, in boron and hydrogen plasmas, is studied. The evolution of the charge state populations of the neutral beams is described considering the various ionization, excitation, and charge exchange channels. The interaction of the beam with the plasma is described in terms of the Fokker–Planck equation, which is numerically solved to show in detail the evolution of the beam until final thermalization is reached. Beam energies of 640 keV/u (maximum of the cross section for the p-B11 fusion reaction) and 200 keV/u, and various plasma temperatures are considered. It is seen that, due to an important perpendicular-diffusion effect, high energy beams reach effective peak temperatures which are much higher than the plasma temperature, before equilibrium is established. The fraction of fusioned particles is also calculated. Some implications of interest for recently proposed p-B11 fusion reactor systems are drawn out.

Spheromak formation and sustainment by tangential boundary flows

The nonlinear, resistive, three-dimensional magnetohydrodynamic equations are solved numerically to demonstrate the possibility of forming and sustaining a spheromak by forcing tangential flows at the plasma boundary. The method can be explained in terms of helicity injection. Several features previously observed in dc helicity injection experiments are reproduced and analyzed.

The effect of ion motion on rotating magnetic field current drive

The effect of ion motion on rotating magnetic field (RMF) current drive in field reversed configurations is studied using a fully two-dimensional numerical code that solves the two fluid equations with massless electrons and constant uniform temperature. The ion momentum equation includes viscosity and collisions with neutrals, which remain fixed. The electrons are described with an Ohms law that includes the Hall and pressure gradient terms. For full penetration of the RMF, ion spin-up due to collisions with electrons reduces the current drive efficiency and a large fraction of neutrals is needed to prevent the ions from acquiring high azimuthal velocities. For conditions that would result in incomplete penetration with the fixed ion model, ion rotation and variable density can facilitate the penetration of the RMF, thus increasing the efficiency. The rotation modifies the density profile and can trigger rotational instabilities.