ALBERT

Notes: Injection of a neutral beam into a plasma in a magnetic field has been studied by means of numerical plasma simulations. It is found that, in the absence of a rotational transform, the convection electric field arising from the polarization charges at the edges of the beam is dissipated by turbulent plasma convection, leading to anomalous plasma diffusion across the magnetic field. The convection electric field increases with the beam density and beam energy. In the presence of a rotational transform, polarization charges can be neutralized by the electron motion along the magnetic field. Even in the presence of a rotational transform, a steady-state convection electric field and hence anomalous plasma diffusion can develop when a neutral beam is constantly injected into a plasma. Theoretical investigations of the convection electric field are described for a plasma in the presence of a rotational transform.

Notes: Injection of a nonrelativistic electron beam into a fully ionized plasma from a spacecraft including the effect of charging has been studied using a one-dimensional particle simulation model. It is found that the spacecraft charging remains negligible and the beam can propagate into a plasma, if the beam density is much smaller than the ambient density. When the injection current is increased by increasing the beam density, significant spacecraft charging takes place and the reflection of beam electrons back to the spacecraft reduces the beam current significantly. On the other hand, if the injection current is increased by increasing the beam energy, spacecraft charging remains negligible and a beam current much larger than the thermal return current can be injected. It is shown that the electric field caused by the beam–plasma instability accelerates the ambient electrons toward the spacecraft thereby enhancing the return current.

Notes: Mode conversion near the upper-hybrid resonance frequency and electron heating are studied using a one-dimensional electromagnetic relativistic particle code. It is found that for a sufficiently small pump field E0, E20/4πnTe (approximately-less-than)0.01, electron heating is localized in a region near the electron cyclotron layer where the pump frequency is equal to the local electron gyrofrequency. For stronger pump fields, electron heating takes place more or less uniformly across a region between the upper-hybrid resonance layer and the cyclotron layer. In addition, a significant fraction of electromagnetic energy associated with the pump is found to be reflected back into the vacuum from a region in the plasma near the upper-hybrid resonance layer for both strong (E20/4πnTe ≈1) and weak pumps (E20/4πnTe (very-much-less-than)1).

Notes: One- and two-dimensional particle simulations of beam–plasma interaction have been carried out in order to understand current drive experiments that use an electron beam injected into the Advanced Concepts Torus (ACT)-1 device [Rev. Sci. Instrum. 53, 409 (1982)]. Typically, the initial beam velocity along the magnetic field is V0=109 cm/sec, while the thermal velocity of the background electrons is vt=108 cm/sec. The ratio of the beam density to the background density is about 10% so a strong beam–plasma instability develops, causing rapid diffusion of beam particles. For both one- and two-dimensional simulations, it is found that a significant amount of beam and background electrons are accelerated considerably beyond the initial beam velocity when the beam density is more than a few percent of the background plasma density. In addition, the electron distribution along the magnetic field has a smooth negative slope, f'(v(parallel))〈0, for v(parallel)〉0 extending to v(parallel)=1.5 V0∼2 V0, which is in sharp contrast to the predictions from quasilinear theory. An estimate of the mean-free path for beam electrons caused by Coulomb collisions reveals that the beam electrons can propagate a much longer distance than is predicted from a quasilinear theory because of the presence of a high-energy tail. These simulation results agree well with the experimental observations from the ACT-1 device.

Notes: Two-dimensional numerical plasma simulations have been carried out in a uniform magnetic field to study the effects of neutral beam injection on plasma diffusion. Neutral beams injected across a magnetic field are assumed to be ionized by various ionization processes in a plasma. It is found that the suprathermal convective motion of a plasma generated by the injection of neutral beams is dissipated via anomalous viscosity, leading to enhanced cross-field diffusion. The diffusion coefficient depends weakly on the magnetic field and plasma density, similar to the diffusion caused by thermally excited convective cells. The magnitude of the diffusion increases with the injection energy and is much larger than the thermal diffusion because of the presence of suprathermal plasma convection. It is shown that a similar anomalous plasma diffusion may occur in a plasma subject to radio frequency (rf) wave heating where only a localized region of a plasma across the magnetic field is heated to a temperature much higher than the surrounding temperature. Theoretical investigations are described on the scaling of enhanced plasma diffusion.

Notes: Propagation of a nonrelativistic electron beam in a plasma in a strong magnetic field has been studied using electrostatic one-dimensional particle simulation models. Electron beams of finite pulse length and of continuous injection are followed in time to study the effects of beam–plasma interaction on the beam propagation. For the case of pulsed beam propagation, it is found that the beam distribution rapidly spreads in velocity space generating a plateaulike distribution with a high energy tail extending beyond the initial beam velocity. This rapid diffusion takes place within a several amplification length of the beam–plasma instability given by (ωpω2b) −1/3V0, where ωp, ωb, and V0 are the target plasma, beam–plasma frequencies, and the beam drift speed. This plateaulike distribution, however, becomes unstable as the high energy tail electrons free-stream, generating a secondary beam. A similar process is observed to take place for the case of continuous beam injection when the beam density is small compared with the total density nb/nt〈1. In particular, the electron velocity distribution is found monotonically decreasing in energy, having a high energy tail whose energy reaches twice the initial beam energy. Such an electron distribution is also seen in laboratory experiments and in computer simulations performed for a uniform, periodic system. When the beam density is increased so that the beam current exceeds the thermal return current, enbV0(approximately-greater-than)enevt, where ne and vt are the density and thermal speed of the ambient electrons, beam propagation becomes much slower due to the electric field generated by the excess charges associated with the beam electrons.Beam electrons are reflected from the ambient plasma as if they are bouncing off a rigid wall. When the beam velocity is increased while holding the beam density constant, simulations show that the beam current can exceed significantly the return current generated by the thermal electrons enevt. It is shown that the electric field generated by the beam–plasma instability accelerates the ambient electrons opposite to the beam propagation, thereby enhancing the return current.

Notes: The diffusion of electrons across a magnetic field in the presence of a beam–plasma instability has been studied by means of two-dimensional numerical simulations. It is found that the beam electrons can diffuse much faster across the magnetic field than the thermal electrons. This can be explained by the fact that the electrons in the beam are in resonance with the waves excited by the beam–plasma instability so that they experience a nearly d.c. electric field, causing large cE×B/B2 excursions.

Notes: Abstract This paper describes the finite element turbulent flow analysis, which is suitable for three-dimensional large scale problems. Thek-ε turbulence model as well as the conservation equations of mass and momentum are discretized in space using rather low order elements. Resulting coefficient matrices are evaluated by one-point quadrature in order to reduce the computational storage and the CPU cost. The time integration scheme based on the velocity correction method is employed to obtain steady state solutions. For the verification of this FEM program, two-dimensional plenum flow is simulated and compared with experiment. As the application to three-dimensional practical problems, the turbulent flows in the upper plenum of the fast breeder reactor are calculated for various boundary conditions.

Notes: Abstract Several numerical plasma simulation models using particles are described which are appropriate for low frequency electrostatic and electromagnetic microinstabilities in a strong magnetic field. The model makes use of the guiding center drift approximations for the electrons while the ions are represented either as particles obeying the equation of motion with the full Lorentz force or a fluid which includes finite-Larmor-radius effects. These models are particularly useful for studying low frequency microinstabilities (ω ≲ ωpi, Ωi) propagating nearly perpendicular to an external magnetic field (k⊥ ≫ k∥).