  Type Ia supernovae (SNe Ia) are standardizable cosmological candles which led
to the discovery of the accelerating universe. However, the physics of how
white dwarfs (WDs) explode and lead to SNe Ia is still poorly understood. The
initiation of the detonation front which rapidly disrupts the WD is a crucial
element of the puzzle, and global 3D simulations of SNe Ia cannot resolve the
requisite length scales to capture detonation initiation. In this work, we
elucidate a theoretical criterion for detonation initiation in the distributed
burning regime. We test this criterion against local 3D driven turbulent
hydrodynamical simulations within electron-degenerate WD matter consisting
initially of pure helium. We demonstrate a novel pathway for detonation, in
which strong turbulent dissipation rapidly heats the helium, and forms carbon
nuclei sufficient to lead to a detonation through accelerated burning via
$\alpha$ captures. Simulations of strongly-driven turbulent conditions lead to
detonations at a mean density of $10^6$ g cm$^{-3}$ and mean temperature of
$1.4 - 1.8 \times 10^9$ K, but fail to detonate at a lower density of $10^5$ g
cm$^{-3}$, in excellent agreement with theoretical predictions.
