4 Effects of varying the proton to electron mass ratio

Given the artificially low mass ratio in our simulations there is a concern about the sensitivity of the results on the value of $m_{\rm p}/m_{\rm e}$. In order to address this question we show the same simulation for two different values of $m_{\rm p}/m_{\rm e}$ in Fig. 8. The other parameters are identical for both simulations , i.e. $\gamma_{\rm p}=4$ and $N=6400$. In both cases the formation of a transonic wind occurs, in association with the formation of a maximum in the proton potential. However, the maximum's amplitude is substantially higher, and less peaked, in the low mass ratio simulation. The discrepancy is likely due to the fact that in the high mass ratio case the scattering of the electrons in velocity space by the protons is more efficient than in the low mass ratio case. Indeed, the temperature ratio $T_{\rm e\parallel}/T_{\rm e\perp}$ reaches a value of 3 at the upper boundary in the $m_{\rm p}/m_{\rm e}=400$ case (cf. Fig. 4) and a value of 4 in the $m_{\rm p}/m_{\rm e}=100$ case. As a result the absolute value of second term on the right hand side of Eq. (9) is significantly smaller in the high mass ratio case than in the low mass ratio case. Since the sign of this term is negative it contributes in reducing the the strength of the overall positive electric field. >From Fig. 4 one may argue that a similar argument applies to the observation that the electric field strength increases with increasing plasma density (i.e. with increasing collisionality) as does effectively show Fig. 1.

Extrapolating these observations to and $N=6400$ one therefore expects the maximum of the proton potential to drop to an even lower level. The peak is expected to be at least as marked as for the $m_{\rm p}/m_{\rm e}=400$ case.