  We use the generalized Chowla-Selberg formula to consider the Casimir effect
of a scalar field with a helix torus boundary condition in the flat
($D+1$)-dimensional spacetime.
  We obtain the exact results of the Casimir energy density and pressure for
any $D$ for both massless and massive scalar fields. The numerical calculation
indicates that once the topology of spacetime is fixed, the ratio of the sizes
of the helix will be a decisive factor. There is a critical value $r_{crit}$ of
the ratio $r$ of the lengths at which the pressure vanishes. The pressure
changes from negative to positive as the ratio $r$ passes through $r_{crit}$
increasingly. In the massive case, we find the pressure tends to the result of
massless field when the mass approaches zero. Furthermore, there is another
critical ratio of the lengths $r_{crit}^{\prime}$ and the pressure is
independent of the mass at $r=r_{crit}^{\prime}$ in the D=3 case.
