How Negative Energy and Kelvin-Helmholtz Instabilities Grow by Longitudinal Waves in Solar Atmospheric Jets

We model the propagation of slow magnetoacoustic body waves in solar jets in the course of negative energy wave excitation in the context of magnetohydrodynamic theory. Explicit approximate expressions are provided for the dispersion relation of slow body waves, providing insight into the influence of the steady flow speed, radiative cooling, and plasma-β at a glance. Analytic expressions are provided regarding critical speeds in the presence of backward waves, negative energy wave speeds, and instabilities. The buildup of the Kelvin-Helmholtz instability above the negative energy wave instability is expressed through analytic expressions that provide insight into the interplay of equilibrium conditions and dispersive effects as they affect the instability growth rate of slow body waves at various altitudes. As slow magnetoacoustic waves propagate with the same speed in the long-wavelength limit, slow body kink waves experience stronger dispersion than sausage waves. Backward waves are also probable at lower steady flow speeds for medium wavelengths when the jet hosts slow body kink waves that provide greater domains for dissipative processes. Slow body sausage waves grow faster while nearing the long-wavelength limit, while the internal plasma-β decreases the instability growth rate. The seismological aspect is that energy transfer to the external medium is observed on various timescales. The observational aspect is that slow body kink waves may exist at higher altitudes as energy has already been extracted to the external medium due to negative energy unstable slow body sausage waves in earlier stages contributing toward coronal heating.