Peristaltic Flow in Compressible, Ideal Magnetohydrodynamics: A Mechanism For Solar Spicules

We present analytical model for peristaltic transport within compressible, ideal magnetohydrodynamics (MHD). By employing small-amplitude perturbation expansion, under thin-tube long-wavelength approximation with a uniform axial background magnetic field, we study non-linear coupling between thermodynamic pressure variations and Maxwell's magnetic tension stresses. The resulting net time-averaged volumetric flow rate $\langle Q \rangle$ is calculated. When applied to solar chromospheric spicules under equipartition constraints ($\beta \sim 1$), where sound speed matches the Alfv{\'e}n speed, we find $\langle Q \rangle = 4\epsilon^2/(M^2-1)$. Because the denominator remains positive across all operational supersonic Mach numbers ($M \approx 2\text{--}10$), upward-propagating mechanical disturbances drive a highly directional, collimated upward flow which we interpret as a spicule. Estimates show that for observationally realistic magnetosonic waves with amplitudes of $\approx 10\%$, the peristaltic mechanism generates a localized mass flux $\approx 100$ times that of solar wind. We propose an explicit observational signature of this mechanism, wherein the launch of individual spicular jets is directly preceded by magnetosonic wave trains detectable as localized intensity modulations. Beyond solar chromospheric application, the model may be applicable to traveling magnetic field pinches in laboratory plasma devices and astrophysical mass-loading processes in stellar winds and inner regions of magnetized accretion disks.