Effect of viscous dissipation on the generation of shear flow at a plasma edge in the finite gyro-radius guiding center approximation

Abstract

A numerical simulation is performed to study the effect of a viscous dissipation term on the generation of shear flow at a plasma edge in the guiding center approximation. The guiding center model includes the effects of finite Larmor radius corrections and polarization drift. The numerical code applies the method of fractional steps to the fluid guiding center equations. We attempt to discriminate between the smoothing of the microstructure by a small viscous dissipation term to control numerical instabilities, and the modification of the macroscopic physical results introduced by this small viscous dissipation term. The finite Larmor radius effect allows for a charge separation to exist, which can be further accentuated by the polarization drift. A difference in the viscous term between electrons and ions can add to the charge separation effect at the plasma edge, which can modify the physical results. The numerical calculation is effected using a slab model, periodic in one direction and finite in the other direction, with an inhomogeneous density of guiding centers to simulate a plasma edge. The evolution of the system shows the potential evolving to a shape characterized by the longest wavelength associated with the transverse dimension of the system, an evolution characteristic of an inverse cascade. We present an analysis of the effect of different values of the viscous term on the time evolution of this guiding center system, and on the formation and existence of a charge separation and an electric field at the edge of a plasma and the associated shear in the E × B flow.

Numerical Solution of the Gyroaverage Operator for the Finite Gyroradius Guiding-Center Model

“…This section is devoted to the coupling of the gyroaverage operator with the guidingcenter model. This model has been introduced in [15] and simulations have been performed in [9,11,14,22]. This model considers the evolution of the guiding-center density f = f (t,x 1 ,x 2 ) in the poloidal plan of the tokamak (see Appendix A for more details on its derivation) supplemented with an initial condition: f (0, x) = f 0 ( x).…”

Charge Separation and Electric Field at a Cylindrical Plasma Edge

“…In previous publications (Shoucri et al, 2003, 2004, Shoucri, 2002, 2008a,b, 2009a the electrons density and temperature profiles were kept constant. In the present work we will allow the electrons to move, and it will be sufficient for the purpose of our study to describe the motion of the electrons, having a small gyroradius, by a guiding center equation (Shoucri et al, 1997). This allows a more accurate description of the contribution of the electrons, with respect to the approximation previously used in Shoucri et al, 2003Shoucri et al, , 2004Shoucri et al, , 2009a, where the profile of the electrons was assumed constant in time.…”

Gyro-kinetic simulation of charge separation and velocity shear at a plasma edge

“…The 2D gyro-kinetic equations are written with the notation of Refs. [1,2]: Eo The star is an abbreviation for an integral operator: a*(y) = SG(y-y')a(y')dy" (4) where G(y) is a Gaussian kernel. In Fourier space, this is equivalent to multiply each coefficient of the e i~'~: mode by a factor Gk = exp l-kZp2~)/2, Pi,e = vti,~ / COci,e.…”

“…These equations are solved using a method of fractional steps which has been previously presented [1,2]. Figure 1 shows the geometry of the problem.…”

“…both ions and electrons are kinetic, the others are obtained from the code where the ions are treated with fluid guiding center equations for the ion density[1,2]. The agreement between the two codes is good.…”