Arbitrary poloidal gyroradius effects in tokamak pedestals and transport barriers

Abstract

Abstract.A technique is developed and applied for analyzing pedestal and internal transport barrier (ITB) regions in a tokamak by formulating a special version of gyrokinetics. In contrast to typical gyrokinetic treatments, canonical angular momentum is taken as the gyrokinetic radial variable rather than the radial guiding center location. Such an approach allows strong radial plasma gradients to be treated, while retaining zonal flow and neoclassical (including orbit squeezing) behavior and the effects of turbulence. The new, nonlinear gyrokinetic variables are constructed to higher order than is typically the case. The nonlinear gyrokinetic equation obtained is capable of handling such problems as collisional zonal flow damping with radial wavelengths comparable to the ion poloidal gyroradius, as well as zonal flow and neoclassical transport in the pedestal or ITB. This choice of gyrokinetic variables allows the toroidally rotating Maxwellian solution of the isothermal tokamak limit to be recovered. More importantly, we prove that a physically acceptable solution for the lowest order ion distribution function in the banana regime anywhere in a tokamak and, in particular, in the pedestal must be nearly this same isothermal Maxwellian solution. That is, the ion temperature variation scale must be much greater than the poloidal ion gyroradius. Consequently, in the banana regime the background radial ion temperature profile cannot have a pedestal similar to that of plasma density.

Zonal flow in a tokamak pedestal

“…However, while a density gradient cannot affect single particle motion directly, it necessarily builds up a strong electric field to sustain pressure balance 15,20 . In a subsonic pedestal with a density gradient as large as 1/ pol ρ , the resulting E B × drift ( E v ) contributes to the poloidal angular velocity θ of ions in leading order so that…”

“…15 that in the banana regime this is the only physically acceptable choice giving no entropy production in the pedestal. This result is also confirmed experimentally by recent measurements in the DIII-D tokamak that found He ion temperature variation much slower than that of the density and electron temperature 16 .…”

“…Recently, some basic features inherent in a pedestal were theoretically found in Ref. 15 . The formalism developed there allows the radial pedestal width to be of the order of ion poloidal gyroradius while assuming pol ρ ρ , where ρ is the ion gyroradius.…”

Enhancement of the Bootstrap Current in a Tokamak Pedestal

“…However, the flows in C-Mod are subsonic so the only way to satisfy radial ion pressure balance is for the ions to be nearly electrostatically confined with a somewhat weaker background ion temperature variation than the density [16]. This weaker ion temperature variation also enhances the bootstrap current and is required to minimize entropy production in the pedestal; however, it is not the primary effect of interest for the discussion that follows.…”

Fully electromagnetic nonlinear gyrokinetic equations for tokamak edge turbulence

“…As emphasized in the previous work on the nonlinear gyrokinetic equations in core transport barriers, 24 a formulation in terms of the radial electric field rather than in terms of mass flow is preferred. Since the single particle's guiding center motion is determined by the electromagnetic field rather than the mass flow, this choice is not only natural, but also advantageous in separating the issue of determining the equilibrium ion distribution function (which is also an important issue at the tokamak edge in its own right 40,41 ) from the formulation of the nonlinear gyrokinetic equation for turbulence. Neoclassical equilibrium, i.e., the distribution function in the absence of the turbulence, in the steep pressure gradient edge region, can be calculated numerically as an input for turbulence simulations.…”