... define

The notation used here differs slightly from that in Brandenburg et al. (2008), where test fields $\overline{\vec{B}}^p$ were originally introduced, and only later were the two versions $\overline{\vec{B}}^{p \rm {c}}$ and $\overline{\vec{B}}^{p \rm {s}}$ considered.

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... obtain

The $\overline{\vec{U}}$ term is incorrect in the corresponding expression (27) of Brandenburg (2005). This did not affect his results, because $\overline{\vec{U}}=0$.

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... ODE

http://www.nordita.org/software/pencil-code

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