The Brunt–Väisälä frequency of rotating tokamak plasmas

Abstract

a b s t r a c tThe continuous spectrum of analytical toroidally rotating magnetically confined plasma equilibria is investigated analytically and numerically. In the presence of purely toroidal flow, the ideal magnetohydrodynamic equations leave the freedom to specify which thermodynamic quantity is constant on the magnetic surfaces. Introducing a general parametrization of this quantity, analytical equilibrium solutions are derived that still posses this freedom. These equilibria and their spectral properties are shown to be ideally suited for testing numerical equilibrium and stability codes including toroidal rotation. Analytical expressions are derived for the low-frequency continuous Alfvén spectrum. These expressions still allow one to choose which quantity is constant on the magnetic surfaces of the equilibrium, thereby generalizing previous results. The centrifugal convective effect is shown to modify the lowest Alfvén continuum branch to a buoyancy frequency, or Brunt-Väisälä frequency. A comparison with numerical results for the case that the specific entropy, the temperature, or the density is constant on the magnetic surfaces yields excellent agreement, showing the usefulness of the derived expressions for the validation of numerical codes.

Continuum modes in rotating plasmas: General equations and continuous spectra for large aspect ratio tokamaks

“…Recently, it has been shown in Ref. 23, that the case when the function p=q C s is constant on the magnetic surface is also integrable (p and q are plasma pressure and mass density, C s is numerical constant). The continuous spectra for such equilibria with the toroidal mass flow have been analyzed in a lot of recent publications.…”

The effect of toroidal plasma rotation on low-frequency reversed shear Alfvén eigenmodes in tokamaks

“…The nested magnetic surfaces, labelled by the poloidal flux function ψ, are assumed to be of constant equilibrium temperature T (ψ) = p/ρ with p and ρ the plasma pressure and density. Within the magnetic surfaces, rotating with angular frequency (ψ), the force balance ∂p/∂R| ψ = ρR 2 is then satisfied by [22,23] …”

“…The toroidal flow-induced continuum gap for −ω − < ω D < ω − is caused by the centrifugal convective effect, whereω − is similar to a buoyancy or Brunt-Väisälä frequency [16,23].…”

Flow shear stabilization of rotating plasmas due to the Coriolis effect

“…Within the magnetic surfaces the force balance is given by ∂p/∂R| ψ = ρR 2 which can be solved analytically by [14] …”

“…The quantity M ≡ R 0 √ ρ 0 /2p 0 is approximately a Mach number. The quantity γ ζ ≡ ζ /(ζ − 1) can be interpreted as the adiabatic constant of the equilibrium [14].…”