  We report on a self-organizing, quasi-stable regime of laser proton
acceleration, producing 1 GeV nano-Coulomb proton bunches from laser foil
interaction at an intensity of 7*10^21 W/cm2. The results are obtained from 2D
PIC simulations, using circular polarized light normally incident on a planar,
500 nm thick hydrogen foil with Gaussian transverse profile. While foil plasma
driven in the wings of the driving pulse is dispersed, a stable central clump
with 1 - 2 lamda diameter is forming on the axis. The stabilisation is related
to laser light having passed the transparent parts of the foil in the wing
region and encompassing the still opaque central clump. This feature is
observed consistently in 2D and 3D simulations. It depends on a laser pulse
shape with high contrast ratio.
