Comprehensive full-f drift-kinetic and delta-f gyrokinetic simulations of a linear plasma device based on the gyro-moment approach

Abstract

First of a kind comprehensive full-f drift-kinetic (DK) and $δ$-f gyrokinetic (GK) turbulent simulations are carried out in a linear plasma device. We self-consistently derive an electrostatic model including large-scale slowly-varying DK-ordered fields coupled to small-scale rapidly-fluctuating GK-ordered fields. By relying on the critical balance ordering, we show that the electrons are described by a drift-reduced Braginskii model while we rely on a Hermite-Laguerre spectral expansion for describing both the DK and GK parts of the ion distribution function. Global simulations are carried out using the parameters of the linear device LAPD, showing that the DK part of the ion distribution function is approximately a bi-Maxwellian. Fast spectral convergence both for the DK and GK Hermite-Laguerre expansion coefficients is observed, and that the GK fields do not affect the DK fields at the physical LAPD collisionality. Only when the collisionality is reduced and the source term is amplified for the GK fluctuations, an amplification of small-scale turbulent structures is observed. The findings are supported by linear results that show that the simulations are dominated by turbulent fluctuations that are Kelvin-Helmholz driven. Additionally, a GK Kelvin-Helmholz-like mode is observed in the low-GK-collisionality regime which can non-linearly drive small-scale structures.

Figures (12)

• Figure 1: The spatial and azimuthal average of the DK moments, $\left\langle \mathcal{N}^{pj}_{iDK} \right\rangle_{t,\vartheta}$, for a full simulation with $\left(P_{DK},J_{DK},P_{GK},J_{GK}\right)=\left(6,3,6,5\right)$ for $p=1-4$ (rows) and $j=1,2$ (columns). Moments with odd $p$ are antisymmetric around $z=L_z/2$ and moments with even $p$ are symmetric around $z=L_z/2$.
• Figure 2: The spatial and azimuthal average of $\mathcal{N}^{pj}_{iGK}$, $\left\langle \mathcal{N}^{pj}_{iGK} \right\rangle_{t,\vartheta}$, for a full simulation with $\left(P_{DK},J_{DK},P_{GK},J_{GK}\right)=\left(6,3,6,5\right)$ for $p=1-4$ (rows) and $j=1,2$ (columns). Moments with odd $p$ are antisymetric around $z=L_z/2$ and moments with even $p$ are symmetric around $z=L_z/2$.
• Figure 3: The spatial maximum of the difference between the DK moments and the moments of a bi-Maxwellian calculated using Eq. (\ref{['eq:bi_Max']}) with the local parallel and perpendicular temperatures normalized to the local density for $\left(P_{DK},J_{DK},P_{GK},J_{GK}\right)=\left(6,3,6,5\right)$. Small deviations from a bi-Maxwellian are observed.
• Figure 4: The azimuthal and temporal average, root mean square, and skewness of $\phi_{DK}$ at $z=L_z/2$ for different choices of $\left(P_{DK},J_{DK},P_{GK},J_{GK}\right)$. For the GK simulations, $P_{DK}=P_{GK}$ and $J_{GK}=5$. The full (solid) and DK (dashed) models are compared. The simulations are considered converged at $\left(P_{DK},J_{DK}\right)=\left(2,1\right)$. The presence of GK fields does not impact $\phi_{DK}$ noticeably.
• Figure 5: Perpendicular, $\left(x,y\right)$, snapshot of $N_{DK}$ (top left), $T_{eDK}$ (top center), $J_{\parallel}$ (top right), $\phi_{DK}$ (bottom left), $\Omega$ (bottom center), and $U_{\parallel}$ (bottom right) for a full simulation with $\left(P_{DK},J_{DK},P_{GK},J_{GK}\right)=\left(6,3,6,5\right)$ at $z=L_z/2$. Turbulent structures are observed at the source-gradient region ($r\sim r_s\sim 20\rho_{s0}$).