= Solution
Both mechanisms can extract <free energy> from an equilibrium <pressure gradient> in unfavorable <magnetic field-line curvature>, but the dynamics retained here is the macroscopic electromagnetic displacement of a <flux tube>. It depends on the total <pressure gradient>, including <electron> and <ion> contributions, and it does not require an <ion temperature gradient> specifically. Its stable branch has $\omega\sim k_\parallel v_A$; with low <plasma beta>, this is much faster than <ion> parallel streaming at the same $k_\parallel$.
The familiar <ion-temperature-gradient instability> is a slower drift-scale instability. In its usual electrostatic ordering the <Boltzmann electron response> is established by rapid <electron> parallel motion, while <ion> magnetic drifts, <ion> temperature evolution and <polarization drift> provide the instability dynamics. A representative ordering is
$$
k_\parallel v_{\mathrm{th},i}\lesssim|\omega|\ll k_\parallel v_{\mathrm{th},e},\qquad
|\omega|\ll k_\parallel v_A,\qquad
\omega_{*T_i}\sim\frac{k_yv_{\mathrm{th},i}^2}{\Omega_iL_{T_i}},\quad
\omega_{di}\sim\frac{k_yv_{\mathrm{th},i}^2}{\Omega_iR}.
$$
The last two expressions specify scales rather than exact geometric factors; $L_{T_i}^{-1}=-d\ln T_{0i}/dx$. The present leading <kinetic magnetohydrodynamics> system drops these relative species drifts and their finite-<gyroradius> corrections. It also retains the perturbed field direction, which enforces the advected-distribution cancellation in <3/c>; a rapid <electron> streaming rate alone cannot turn that cancellation into a <Boltzmann electron response> on an unperturbed field.
To recover <ion-temperature-gradient instability> physics, take the slow, nearly electrostatic limit $|\omega|/(k_\parallel v_A)\ll1$, retain <magnetic curvature drift>, <gradient-B drift> and <polarization drift> in low-flow <drift kinetics> or <gyrokinetics>, and allow a sufficiently strong destabilizing <ion temperature gradient>. At long perpendicular <wavelengths> one may still have $k_\perp\rho_i\ll1$, provided the leading nonzero <ion> polarization is kept; at $k_\perp\rho_i=O(1)$ full <finite Larmor radius effects> are needed. There is no contradiction between a drift-scale <ion-temperature-gradient instability> and the macroscopic <interchange instability> derived here: they use different asymptotic balances.
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