We have performed self-consistent 2.5-dimensional nonsteady MHD numerical simulations of jet formation as long as possible , including the dynamics of accretion disks .
Although the previous nonsteady MHD simulations for astrophysical jets revealed that the characteristics of nonsteady jets are similar to those of steady jets , the calculation time of these simulations is very short compared with the time scale of observed jets .
Thus we have investigated long term evolutions of mass accretion rate , mass outflow rate , jet velocity , and various energy flux .
We found that the ejection of jet is quasi-periodic .
The period of the ejection is related to the time needed for the initial magnetic filed to be twisted to generate toroidal filed

T _ { ejection } \propto \frac { 1 } { V _ { A } } \propto \frac { 1 } { B } \propto E ^ { - \frac { 1 } { 2 } } _ { % mg } . We compare our results with both the steady state theory and previous 2.5-dimensional nonsteady MHD simulations .
Then it is found that time averaged velocity of jets ( V _ { jet \hskip { 2.845276 pt } \mathrm { ave } } ) are \sim 0.1 V _ { \mathrm { K } } and \sim 0.1 V _ { jet \hskip { 2.845276 pt } \mathrm { max } } , where V _ { \mathrm { K } } is the Keplerian velocity at ( r,z ) = ( 1 , 0 ) and V _ { jet \hskip { 2.845276 pt } \mathrm { max } } is the maximum velocity of jet .
Nevertheless , the characteristics of our simulations are consistent with those of steady solution and previous short term simulations in that the dependences of the time averaged velocity V _ { z \hskip { 2.845276 pt } \mathrm { ave } } and mass outflow rate \dot { M } _ { w \hskip { 2.845276 pt } \mathrm { ave } } on the initial magnetic field strength are approximately

\dot { M } _ { w \hskip { 2.845276 pt } \mathrm { ave } } \propto B ^ { 0.32 } \hskip { 14.226378 pt } % \mathrm { and } \hskip { 14.226378 pt } V _ { jet \hskip { 2.845276 pt } \mathrm { ave } } \propto { B _ % { 0 } } ^ { 0.3 } .