Table 1: Values of the parameters for the spherical model (KC) and for two different set up of our axisymmetric RMHD simulations, runA (1) and runA (2). $A_{\rm r}$ is in unit ${\rm cm^{-3}}$ and $A_{\rm w}$ is in unit ${\rm erg^{-1}}$ .
Parameters KC RunA (1) RunA (2)

$\alpha_{{\rm r}}$ 0.26 0.26 0.26

$\alpha_{\rm w}$ 0.70 0.70 0.85

$A_{\rm r}$ $2.90\times 10^{-6}$ $1.35\times 10^{-5}$ $1.35\times 10^{-5}$

$A_{\rm w}$ $3.2\times 10^{8}$ $2.6\times10^{9}$ $3.2\times10^{11}$

$\epsilon^{*}_{{\rm r}}$ $2.0\times 10^{5}$ $3.0\times10^{5}$ $3.0\times10^{5}$

$\epsilon^{*}_{{\rm w}}$ $1.4\times 10^{10}$ $\infty$ $\infty$

$\bar{\epsilon}$ $4.3\times 10^{5}$ $5.0\times 10^{5}$ $8.0\times10^{5}$

**Table 1:** Values of the parameters for the spherical model (KC) and for two different set up of our axisymmetric RMHD simulations, runA (1) and runA (2). $A_{\rm r}$ is in unit ${\rm cm^{-3}}$ and $A_{\rm w}$ is in unit ${\rm erg^{-1}}$ .
Parameters	KC	RunA (1)	RunA (2)
$\alpha_{{\rm r}}$	0.26	0.26	0.26
$\alpha_{\rm w}$	0.70	0.70	0.85
$A_{\rm r}$	$2.90\times 10^{-6}$	$1.35\times 10^{-5}$	$1.35\times 10^{-5}$
$A_{\rm w}$	$3.2\times 10^{8}$	$2.6\times10^{9}$	$3.2\times10^{11}$
$\epsilon^{*}_{{\rm r}}$	$2.0\times 10^{5}$	$3.0\times10^{5}$	$3.0\times10^{5}$
$\epsilon^{*}_{{\rm w}}$	$1.4\times 10^{10}$	$\infty$	$\infty$
$\bar{\epsilon}$	$4.3\times 10^{5}$	$5.0\times 10^{5}$	$8.0\times10^{5}$

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