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Initial Conditions for Lunar Impact Magnetization

Based on the impactor conditions from Oran et al. (2020) https://advances.sciencemag.org/content/6/40/eabb1475 and its supplementary material https://advances.sciencemag.org/content/suppl/2020/09/28/6.40.eabb1475.DC1/abb1475_SM.pdf we have most impact plasma conditions apart from the magnetic field (which they do not seem to inject by any mechanism).

Impact Plasma conditions from iSALE-2D :

Initial Vapour temperature: 2000 K (varies down to 500 K for some models)

Wind Speed: 400 km/s to 1000 km/s

Wind Density: Plots in S4, but no analytical form. Looks proportional to y.

Magnetic field: Probably several equations work.

Assuming the field distribution is similar to that of a very thick (radius s_0 ), finite length ( z_0 ), current carrying wire, the field and vector potential in cylindrical coordinates are:

\mathbf{J}(s) = \begin{cases} \frac{I_0}{2 \pi s_0^2} \, & ; & \quad s \le s_0, \ 0 \le z \le z_0 \\ 0 \, & ; &\quad\text{otherwise.} \\ \end{cases}

\mathbf{A}(s,z) = \begin{cases} \frac{\mu_0 I_0}{4 \pi} \ln \left[ \frac{z_2+\sqrt{s^2+z_2^2}}{z_1+\sqrt{s^2+z_1^2}} \right] \hat{z} &; & \quad s > s_0, \ \text{or} z < 0, \ \text{or} z > z_0 \\ \frac{\mu_0 I_0 s^2}{4 \pi s_0^2} \ln \left[ \frac{z_2+\sqrt{s^2+z_2^2}}{z_1+\sqrt{s^2+z_1^2}} \right] \hat{z} &; &\quad\text{otherwise.} \\ \end{cases}

\mathbf{B}(s,z) = \begin{cases} \frac{\mu_0 I_0}{4 \pi s} \left[ \frac{z_2}{\sqrt{s^2+z_2^2}} - \frac{z_1}{\sqrt{s^2+z_2^1}} \right] \hat{\phi} &; & \quad s > s_0, \ \text{or} z < 0, \ \text{or} z > z_0 \\ \frac{\mu_0 I_0 s}{4 \pi s_0^2} \left[ \frac{z_2}{\sqrt{s^2+z_2^2}} - \frac{z_1}{\sqrt{s^2+z_2^1}} \right] \hat{\phi} &; &\quad\text{otherwise.} \\ \end{cases}

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Initial Conditions for Lunar Impact Magnetization

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