Hugo Ferrari

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.

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.

Impact of the Eulerian chaos of magnetic field lines in magnetic reconnection

Stochasticity is an ingredient that may allow the breaking of the frozen-in law in the reconnec-tion process. It will first be argued that non-ideal effects may be considered as an implicit way to introduce stochasticity. Yet there also exists an explicit stochasticity that does not require the invocation of non-ideal effects. This comes from the spatial (or Eulerian) chaos of magnetic field lines that can show up only in a truly three-dimensional description of magnetic reconnection since two-dimensional models impose the integrability of the magnetic field lines. Some implications of this magnetic braiding, such as the increased particle finite-time Lyapunov exponents and increased acceleration of charged particles, are discussed in the frame of tokamak sawteeth that form a laboratory prototype of spontaneous magnetic reconnection. A justification for an increased reconnection rate with chaotic vs integrable magnetic field lines is proposed. Moreover, in 3D, the Eulerian chaos of magnetic field lines may coexist with the Eulerian chaos of velocity field lines, that is more commonly named turbulence.

Neutral beam injection in a D?3He FRC reactor

The use of neutral beam injection (NBI) to sustain a fraction of the plasma current in a field reversed configuration (FRC) reactor operating with the D–3He reaction is studied. A Monte Carlo code already used to study NBI in medium size FRCs is employed (Lifschitz A F, Farengo R and Arista N R 2002 Nucl. Fusion 42 863, Lifschitz A F, Farengo R and Arista N R 2002 Plasma Phys. Control. Fusion 44 1979, Lifschitz A F, Farengo R and Hoffman A L 2004 Nucl. Fusion 44 1015) and the plasma parameters are similar to those proposed in the ARTEMIS (Momota H, Ishida A, Kohzaki Y, Miley G, Ohi S, Ohnishi M, Sato K, Steinhauer L, Tomita Y and Tuszewki M 1992 Fusion Technol. 21 2307) conceptual reactor design. A simple analysis shows that the driven current cannot reach the values quoted in the ARTEMIS project and a procedure to search for plasma parameters that result in higher efficiencies is presented.

Current drive and heating by fusion protons in a D?3He FRC reactor

The possibility of using the 14.7 MeV protons produced in the D-3 He fusion reaction to sustain the current and heat the plasma in a field reversed configuration reactor is investigated. A Monte Carlo code that includes particle drag and pitch angle scattering is employed to follow the trajectories of the fusion born protons and calculate the resulting current and deposited power. It is found that for the parameters of the proposed ARTEMIS (Momota et al 1992 Fusion Technol. 21 2307) conceptual reactor design a significant current (40–46 MA) could result, depending on the plasma current induced by the protons, which is not calculated. The effect of changing the shape of the plasma equilibrium is also investigated.

Electron inertial effects on rotating magnetic field current drive

The effect of finite electron mass on the formation and sustainment of a field reversed configuration (FRC) by rotating magnetic fields (RMF) is studied. The importance of inertial effects is measured by the ratio between the RMF frequency (ω) and the electron-ion collision frequency (ν). In the limit where this ratio is very small (ω∕ν→0), previous results corresponding to massless electrons are recovered. When ω∕ν increases there are significant changes in the value of the minimum external rotating field needed to sustain the FRC and the time required to reach a steady state. Since ν decreases with increasing temperature and decreasing density, these effects are expected to become more important as fusion relevant temperatures are approached.

Energy and frequency dependence of the alpha particle redistribution produced by internal kink modes

The redistribution of alpha particles due to internal kink modes is studied. The exact particle trajectories in the total fields, equilibrium plus perturbation, are calculated. The equilibrium has circular cross section and the plasma parameters are similar to those expected in ITER. The alpha particles are initially distributed according to a slowing down distribution function and have energies between 18 keV and 3.5 MeV. The (1, 1), (2, 2), and (2, 1) modes are included and the effect of changing their amplitude and frequency is studied. When only the (1, 1) mode is included, the spreading of high energy ( E≳1 MeV) alpha particles increases slowly with the energy and mode frequency. At lower energies, the redistribution is more sensitive to the mode frequency and particle energy. When a (2, 1) mode is added, the spreading increases significantly and particles can reach the edge of the plasma. Trapped particles are the most affected and the redistribution parameter can have maxima above 1 MeV, depending ...

FUSION PARTICLES AND NEUTRAL BEAMS IN FRC REACTORS

Abstract We study the interaction of fusion-born particles and neutral beams (NBs) with field-reversed configuration (FRC) plasmas. The power deposited and the current generated are calculated for FRC reactors operating with the D-T and D-3He fusion reactions. In the beam studies we specify the beam energy and current, the injection point, and the impact parameter and include an ionization package to determine the position and velocity of the beam particles when they become ionized. In the case of fusion-born particles, we consider a large number of isotropic particle sources distributed inside the FRC. The plasma equilibria are obtained by solving the Grad-Shafranov equation with a pressure that contains linear and quadratic terms in the flux function. A Monte Carlo code that includes particle drag and diffusion is then employed to follow the exact trajectories of the fusion or beam particles and calculate the resulting current and deposited power. The effect of a rotating magnetic field and a toroidal field on the current and deposited power is also studied. In D-T reactors the current generated by the alpha particles is small, but the deposited power fraction is large, and NBs can produce significant currents with reasonable input powers. In D-3He reactors the fusion protons can produce large currents, but the deposited power fraction and the NB current drive efficiencies are low. A small toroidal field, compatible with high β FRCs, reduces the deposited power fraction and the current.

Theoretical Analysis of Formation and Sustainment Methods for Compact Toroids

Recent theoretical studies on the use of neutral beams (NB), rotating magnetic fields (RMF) and helicity injection (HI) to form and sustain compact toroids are reported. A Monte Carlo code was employed to study NB injection in Field Reversed Configurations (FRC) and Spheromaks. The code calculates the ionization of the neutral particles and follows the exact orbits of the ions. The magnetic field and density profiles are determined by solving a Grad-Shafranov equation that includes the beam current. RMF current drive in FRCs was studied using a fully 2D code that solves the two fluid equations with massless electrons and uniform temperature. The ion momentum equation includes viscosity and collisions with electrons and neutrals. The electrons are described using an Ohms law with the Hall and pressure gradient terms. Ion spin up due to collisions with electrons reduces the current drive efficiency and a large fraction of neutrals is needed to keep the azimuthal ion velocity small. The principle of minimum rate of energy dissipation was employed to calculate relaxed states for a flux core spheromak sustained by helicity injection. States with large regions of closed flux surfaces and significant toroidal current were found. Changing the resistivity profile modifies the safety factor profile, which can change from one that has a maximum at the magnetic axis (for uniform resistivity) to a tokamak-like q-profile.