Reality of inverse cascading in neutron star crusts

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Table 2.

Summary of the PENCIL CODE simulations.

Run	Geom/B.C.	r/R	θ/π	ϕ/π	$ℓ_{0} ({\tilde{t}}_{0})$ $\ell_0(\tilde{t}_0)$	$ℓ_{0} ({\tilde{t}}_{2})$ $\ell_0(\tilde{t}_2)$	$Lu ({\tilde{t}}_{1})$ $\mathrm{Lu}(\tilde{t}_1)$	$Lu ({\tilde{t}}_{2})$ $\mathrm{Lu}(\tilde{t}_2)$	$k_{0} ξ ({\tilde{t}}_{0})$ $k_0\xi (\tilde{t}_0)$	$χ ({\tilde{t}}_{0})$ $\chi(\tilde{t}_0)$	Mesh points
R1	Cart/PC-VF	0.9–1	0–1	0–1	200	50	260	132	0.50	1.19	64 × 2048²
R2	Sph/PC-VF	0.9–1	0.1–0.9	0–1	200	60	251	124	0.60	1.12	64 × 2048²
R3	Cart/PC-VF	0.8–1	0–1	0–1	200	30	361	202	0.61	1.16	128 × 2048²
R4	Cart/PC-VF	0.8–1	0–0.5	0–0.5	200	10	487	272	0.61	1.15	128 × 1024²
R5	Cart/PC-VF	0.8–1	0–0.5	0–0.5	50	10	724	464	0.46	0.87	128 × 1028²
R6	Cart/P	0.9–1	0–1	0–1	200	60	283	168	0.61	1.19	64 × 2048²

Notes. Cartesian simulations are indicated by ‘Cart’, while spherical simulations are denoted by ‘Sph’. Simulations with perfect conductor boundary conditions on the inner surface and vertical field boundary conditions on the outer surface in the radial directions are labeled as ‘PC-VF’. By contrast, simulations with periodic boundary conditions in the radial directions are labeled as ‘P’. Data is shown at specific times: ${\tilde{t}}_{1} = η t_{1} / R^{2} = 2 \times 10^{- 6}$ $\tilde{t}_1=\eta t_1/R^2 = 2 \times 10^{-6}$ and ${\tilde{t}}_{2} = η t_{2} / R^{2} = 2 \times 10^{- 5}$ $\tilde{t}_2=\eta t_2/R^2 = 2 \times 10^{-5}$ . We note that ℓ₀ = k₀R for the Cartesian runs.

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