J. N. Leboeuf

Dynamic magnetic x points

Two‐and‐one‐half dimensional magnetostatic and electromagnetic particle simulations of time‐varying magnetic x points and the associated plasma response are reported. The stability and topology depend on the geometry, irrespective of the plasma β. The electrostatic field and finite Larmor radius effects play an important role in current penetration and shaping of the plasma flow. The snapping of the field lines, and dragging of the plasma into, and confinement of the plasma at, an o point (magnetic island) is observed. Magnetic island coalescence with explosive growth of the coalescence mode occurs and is accompanied by a large increase in kinetic energy and temperature as well as the formation of hot tails on the distribution functions.

A magnetohydrodynamic particle code for fluid simulation of plasmas

Abstract A novel Lagrangian type of MHD code has been developed by treating elements of the fluid as finite-sized particles. The particle quantities, i.e., position, mass, momentum and temperature, are pushed in a Lagrangian way, while the magnetic fields are advanced in an Eulerian manner. The fully Lagrangian fluid is represented by a distribution of Gaussian-shaped particles. Drag forces between particles with different velocities in the same cell prevent extensive mufti-streaming from developing. A combination of finite differences, to calculate the magnetic field, and fast Fourier transforms, to evaluate the pressure gradient term, guarantees momentum and magnetic flux conservation. The use of particles eliminates many difficulties often associated with Eulerian codes such as, for example; negative densities. The method also means that any particle code of which there are many can be converted to a fluid code. The codes have been extensively tested with the propagation of sound waves, Alfven and magnetosonic waves among others. Applications of the codes to hydrodynamics and magnetohydrodynamics in one, two and three dimensions, in cartesian as well as in toroidal geometry, are further discussed.

Comparison of turbulence measurements from DIII-D low-mode and high-performance plasmas to turbulence simulations and models

Measured turbulence characteristics (correlation lengths, spectra, etc.) in low-confinement (L-mode) and high-performance plasmas in the DIII-D tokamak [Luxon et al., Proceedings Plasma Physics and Controlled Nuclear Fusion Research 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159] show many similarities with the characteristics determined from turbulence simulations. Radial correlation lengths Δr of density fluctuations from L-mode discharges are found to be numerically similar to the ion poloidal gyroradius ρθ,s, or 5–10 times the ion gyroradius ρs over the radial region 0.2<r/a<1.0. Comparison of these correlation lengths to ion temperature gradient gyrokinetic simulations (the UCLA-University of Alberta, Canada UCAN code [Sydora et al., Plasma Phys. Controlled Fusion 38, A281 (1996)]) shows that without zonal flows simulation values of Δr are very long, spanning much of the 65 cm minor radius. With zonal flows included, these decrease to near the measured values in both magnitud...

Linear analysis of sheared flow stabilization of global magnetohydrodynamic instabilities based on the Hall fluid model

A systematic study of the linear stage of sheared flow stabilization of Z-pinch plasmas based on the Hall fluid model with equilibrium that contains sheared flow and an axial magnetic field is presented. In the study we begin with the derivation of a general set of equations that permits the evaluation of the combined effect of sheared flow and axial magnetic field on the development of the azimuthal mode number m=0 sausage and m=1 kink magnetohydrodynamic (MHD) instabilities, with the Hall term included in the model. The incorporation of sheared flow, axial magnetic field, and the Hall term allows the Z-pinch system to be taken away from the region in parameter space where ideal MHD is applicable to a regime where nonideal effects tend to govern stability. The problem is then treated numerically by following the linear development in time of an initial perturbation. The numerical results for linear growth rates as a function of axial sheared flow, an axial magnetic field, and the Hall term are reported.

Search for the ion temperature gradient mode in a tokamak plasma and comparison with theoretical predictions

In recent experiments in DIII-D, comparison of specific turbulence characteristics with linear and nonlinear modeling has identified common features associated with the ion temperature gradient (ITG) mode. A low-frequency turbulence feature is observed in high-density saturated Ohmic confinement discharges, which is absent in low-density linear Ohmic confinement discharges. The feature is in a range of wavelength (k⊥ρs≈0.2–0.5) and the frequency expected for the ITG mode and onset of the feature is coincident with onset of confinement saturation. The density profile is significantly broader in the high-density discharge, a known destabilizing effect on the ITG mode. Gyrokinetic stability calculations of the growth rate of the most unstable drift ballooning mode show the ITG mode to be more unstable in the high-density discharges.

Kelvin–Helmholtz instability in supersonic and super‐Alfvénic fluids

A magnetohydrodynamic particle code is used to simulate highly nonlinear stages of the Kelvin–Helmholtz instability. Without a magnetic field, a supersonic flow with sonic Mach number Ms creates a stream of vortices which turn into a series of structured shock fronts with shock angle sin−1 (1/Ms). With a magnetic field, a super‐Alfvenic flow results in substantial bending of the magnetic field lines.

Magnetohydrodynamic particle code: Lax-Wendroff algorithm with finer grid interpolations

Two marked improvements of algorithms for the magnetohydrodynamic particle code which treats elements of the fluid as finite-size particles are reported. First a Lax-Wendroff algorithm is introduced in the magnetic field pusher making the code nearly dissipationless. Second, a number of improvements to the sharpness of the mode spectra, reduction of noise, dispersion, numerical heating of fluid elements, and improved stability have been achieved by various choices of the methods for assignment of particle quantities to grid points and interpolation of grid quantities at the particle positions. Properties of the various versions of the code have been studied and compared. Applications to the ballooning mode instability, to the endloss problem of a high-beta plasma column with sharp boundaries, and to global MHD simulations of the magnetosphere are presented.

Full torus Landau fluid calculations of ion temperature gradient-driven turbulence in cylindrical geometry

Results of Landau fluid calculations of ion temperature gradient-driven turbulence in cylindrical geometry but which cover the whole plasma cross section are reported. A simple gyrofluid model is used which evolves in time equations for the ion density or vorticity, the parallel ion velocity, and the ion temperature where Landau damping is included through a linear closure relation. Adiabatic electrons and the electrostatic approximation are assumed to hold. Linear calculations indicate that the growth rates are significantly reduced in the presence of Landau damping. Nonlinear single helicity calculations serve to illustrate the spatial localization of the turbulence in the presence of Landau damping. Finally nonlinear multiple helicity calculations performed with three different values for the ratio of the central ion Larmor radius to the plasma minor radius denoted by ρ* exhibit a definite linear scaling of all the fluctuation characteristics, such as levels, scale sizes, quasilinear profile modificati...

A vlasov particle ion zero mass electron model for plasma simulations

Abstract We have extended a particle-MHD model of discrete fluid ions and massless fluid electrons to the fully kinetic ions and massless fluid electrons so that such important kinetic effects, e.g., the finite Larmor radius effects, are incorporated; 2D as well as 3D versions exist. As a result the model now exhibits ion Bernstein waves. We have also developed a linear theory of the model and obtained the linear dispersion relation. The dispersion relation is in excellent agreement with results from the model. Two important improvements in numerical procedures have been implemented; the first is the elimination of unphysical short wavelength disturbances by a smoothing technique; the second is the implementation of the Richardson extrapolation (extrapolation to Δt = 0) technique in the velocity difference equations. These improvements increased the range of stability of the code greatly and enabled us to use time steps which are 10 times larger. As one application, we use the model to simulate the interaction of a neutral gas and an ambient plasma and observe the generation of waves with frequencies at integral as well as half-integral ion cyclotron harmonics for all k in accordance with some recent experimental observations in the JET tokamak.

Development of global magnetohydrodynamic instabilities in Z-pinch plasmas in the presence of nonideal effects

The development of global magnetohydrodynamic (MHD) instabilities in Z-pinch plasmas has been studied with a three-dimensional hybrid simulation model. Plasma equilibria without and with axial sheared flow, and with different values of the parameter eH, which appears as a coefficient before the Hall term in dimensionless nonideal MHD equations, have been considered. Increasing the parameter eH leads to larger simulation growth rates for both m=0 sausage and m=1 kink modes. The hybrid simulations do however show that axial sheared flow severely curtails the linear and nonlinear development of both sausage and kink instabilities. In these respects, the hybrid simulations are in qualitative agreement with linear Hall MHD results. Moreover, in the nonlinear stage, long wavelength modes dominate the excited wave spectrum when the parameter eH is small. For the larger value of the parameter eH, small-scale structures do however develop nonlinearly in the excited wave spectrum at late times.