  We compute the closed-string cylinder amplitude between one Dp brane and the
other Dp$\prime$ brane, placed parallel at a separation, with each carrying a
general constant worldvolume flux and with $p - p' = 0, 2, 4, 6$ and $p \le 6$.
For the $p = p'$, we show that the main part of the amplitude for $p = p' < 5$
is a special case of that for $p = p' = 5$ or $6$ case. For all other $p - p' =
2, 4, 6$ cases, we show that the amplitude is just a special case of the
corresponding one for $p = p'$ case. Combining both, we obtain the general
formula for the amplitude, which is valid for each of the cases considered and
for arbitrary constant worldvolume fluxes. The corresponding general open
string one-loop annulus amplitude is also obtained by a Jacobi transformation
of the general cylinder one. We give also the general open string pair
production rate. We study the properties of the amplitude such as the nature of
the interaction, the open string tachyonic instability, and the possible open
string pair production and its potential enhancement. In particular, in the
presence of pure magnetic fluxes or magnetic-like fluxes, we find that the
nature of interaction is correlated with the existence of potential open string
tachyonic instability. When the interaction is attractive, there always exists
an open string tachyonic instability when the brane separation reaches the
minimum determined by the so-called tachyonic shift. When the interaction is
repulsive, there is no such instability for any brane separation. We also find
that the enhancement of open string pair production, in the presence of pure
electric fluxes, can occur only for the $p - p' = 2$ case.
