  We investigate analytically and numerically the semi-collisional regime of
the plasmoid instability, defined by the inequality $\delta_{SP} \gg \rho_s \gg
\delta_{in}$, where $\delta_{SP}$ is the width of a Sweet-Parker current sheet,
$\rho_S$ is the ion sound Larmor radius, and $\delta_{in}$ is width of boundary
layer that arises in the plasmoid instability analysis. Theoretically, this
regime is predicted to exist if the Lundquist number $S$ and the length of the
current sheet $L$ are such that $(L/\rho_S)^{14/9} < S <(L/\rho_S)^2$ (for a
sinusoidal-like magnetic configuration; for a Harris-type sheet the lower bound
is replaced with $(L/\rho_S)^{8/5}$). These bounds are validated numerically by
means of simulations using a reduced gyrokinetic model (Zocco & Schekochihin,
$\it{Physics~of~Plasmas}$, ${\bf 18}$, 2011) conducted with the code
$\tt{Viriato}$. Importantly, this regime is conjectured to allow for plasmoid
formation at relatively low, experimentally accessible, values of the Lundquist
number. Our simulations obtain plasmoid instability at values of $S$ as low as
$\sim 250$. The simulations do not prescribe a Sweet-Parker sheet; rather, one
is formed self-consistenly during the nonlinear evolution of the initial
tearing mode configuration. This proves that this regime of the plasmoid
instability is realizable, at least at the relatively low values of the
Lundquist number that are accessible to current dedicated experiments.
