Numerical studies of a steady state axisymmetric co-axial helicity injection plasma

Abstract

Steady state current profile, plasma potential, and plasma flow of an electrostatically driven co-axial helicity injection (CHI) plasma with axisymmetry are numerically investigated using both an open field line Grad–Shafranov equilibrium model and self-consistent initial value magnetohydrodynamic (MHD) simulations. For CHI plasmas, the Grad–Shafranov model ignores plasma inertia but not a perpendicular, or Grad–Shafranov, flow. The Grad–Shafranov flow is the result of the gradient of Grad–Shafranov potential across magnetic field lines, and is responsible for toroidal current drive. Numerical Grad–Shafranov solutions show that as the characteristic CHI discharge parameter, the normalized voltage V̂≡μ0V/ηB0q0, becomes order of unity, CHI plasma develops kink-unstable hollow current profile. Here 𝒱 is the imposed voltage, η the plasma resistivity, q0 the toroidal and injector poloidal flux ratio, and B0≡4χ0/ab a nominal poloidal field defined by the injector poloidal flux χ0, plasma minor radius a, and plasma elongation b/a. When a small plasma inertia is included in the equation of motion, such as that in a time dependent MHD calculation, the modification on the perpendicular current is small, but its impact on parallel current distribution and hence the spatial dependence of magnetic flux can be great through the Pfirsch–Schlüter-like effects.