The screw pinch (cylindrical geometry with a magnetic field including axial and azimuthal components) is a simple magnetic configuration that allows studying instabilities in a simplified geometry without toroidal curvature.
This geometry was used to compare the codes EUTERPE (linear code designed for general 3D geometry) and TORB (nonlinear code in screw pinch geometry) in both linear and nonlinear settings in [Sánchez et al. IEETPS 2010]. In this geometry, the formation of zonal flows during the nonlinear saturation of ion temperature gradient (ITG) instabilities is observed. It was shown that β affects the formation of zonal flows, whose amplitude is reduced as beta increases.
Figures 1 and 2 show the amplitude of potential in nonlinear electrostatic simulations in a screw pinch with rotational transform 0.8, and with β=0 and 5%, respectively. In these simulations, the electrons are adiabatic and ions are the only kinetic species. Ideal profiles with a sharp gradient at the middle radius are used.
After a linear phase of exponential growth of the unstable modes, a zonal structure (zonal flow) develops in the potential starting at the middle radius and spreading out both inward and outward as the simulation evolves. The zonal structure is affected by the finite beta value.
In Figure 3, the potential is shown for a simulation with beta=0 and magnetic shear 0.4. [Sanchez et al EPS 2011].