  The hose instability of the drive beam constitutes a major challenge for the
stable operation of plasma wakefield accelerators (PWFAs). In this work, we
show that drive beams with a transverse size comparable to the plasma blowout
radius generate a wake with a varying focusing along the beam, which leads to a
rapid detuning of the slice-betatron oscillations and suppresses the
instability. This intrinsic stabilization principle provides an applicable and
effective method for the suppression of the hosing of the drive beam and allows
for a stable acceleration process.
