  Plasma turbulence is the dominant transport mechanism for heat and particles
in magnetized plasmas in linear devices and tokamaks, so the study of
turbulence is important in limiting and controlling this transport. Linear
devices provide an axial magnetic field that serves to confine a plasma in
cylindrical geometry as it travels along the magnetic field from the source to
the strike point. Due to perpendicular transport, the plasma density and
temperature have a roughly Gaussian radial profile with gradients that drive
instabilities, such as resistive drift-waves and Kelvin-Helmholtz. If unstable,
these instabilities cause perturbations to grow resulting in saturated
turbulence, increasing the cross-field transport of heat and particles. When
the plasma emerges from the source, there is a time, $\tau_{\parallel}$, that
describes the lifetime of the plasma based on parallel velocity and length of
the device. As the plasma moves down the device, it also moves azimuthally
according to $E\times B$ and diamagnetic velocities. There is a balance point
in these parallel and perpendicular times that sets the stabilisation
threshold. We simulate plasmas with a variety of parallel lengths and magnetic
fields to vary the parallel and perpendicular lifetimes, respectively, and find
that there is a clear correlation between the saturated RMS density
perturbation level and the balance between these lifetimes. The threshold of
marginal stability is seen to exist where
$\tau_{\parallel}\approx11\tau_{\perp}$. This is also associated with the
product $\tau_{\parallel}\gamma_*$, where $\gamma_*$ is the drift-wave linear
growth rate, indicating that the instability must exist for roughly 100 times
the growth time for the instability to enter the non-linear growth phase. We
explore the root of this correlation and the implications for linear device
design.
