understanding of the fundamental physical processes responsible for the evolution observed in more complex numerical models.

The present study is organised as follows: in Sect. \[sec:PaperI\] we first quickly synthesise the results of the preceding study of this series [@Pariat15a] and in Sect. \[sec:Model\] we summarise the main set-up of our numerical model. We then successively discuss the influence of the plasma $\beta$ on the trigger of straight and [[helical jets]{}]{}(Sect. \[sec:Trig\]), the driving mechanism (Sect. \[sec:Betadriver\]), and morphological properties (Sect. \[sec:Betamorpho\]) of [[helical jets]{}]{}. Finally, we discuss the implications of our findings in Sect. \[sec:Concl\].

Summary of the results of Paper I {#sec:PaperI}
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In our previous studies we introduced a model that explains morphologically different 3D coronal jets, both straight and helical. An example of the time-evolution of the system in one of the parametric simulations of this study is presented in Fig. \[FigEvolBeta0025\]. Other examples of such dynamics with slightly different conditions can be found in Fig. 4 of @Pariat09a [PAD09] Fig. 2 of @Pariat15a [PDD15], and Fig. 1 of @Pariat15b. The basic physics of our model is that a straight jet is due to slow interchange reconnection between the closed flux of an embedded bipole region 