We analyze the use of a relativistic laser pulse with a controlled frequency
chirp incident on a rising plasma density gradient to drive an acceleration
structure for proton and light-ion acceleration. The Chirp Induced Transparency
Acceleration (ChITA) scheme is described with an analytical model of the
velocity of the snowplow at critical density on a pre-formed rising plasma
density gradient that is driven by a positive-chirp in the frequency of a
relativistic laser pulse. The velocity of the ChITA-snowplow is shown to depend
upon rate of rise of the frequency of the relativistic laser pulse represented
by $\frac{\epsilon_0}{\theta}$ where, $\epsilon_0 =
\frac{\Delta\omega_0}{\omega_0}$ and chirping spatial scale-length, $\theta$,
the normalized magnetic vector potential of the laser pulse $a_0$ and the
plasma density gradient scale-length, $\alpha$. We observe using 1-D OSIRIS
simulations the formation and forward propagation of ChITA-snowplow, being
continuously pushed by the chirping laser at a velocity in accordance with the
analytical results. The trace protons reflect off of this propagating snowplow
structure and accelerate mono-energetically. The control over ChITA-snowplow
velocity allows the tuning of accelerated proton energies.