  Active plasma lenses are compact devices developed as a promising
beam-focusing alternative for charged particle beams, capable of short focal
lengths for high-energy beams. We have previously shown that linear magnetic
fields with gradients of around 0.3 kT/m can be achieved in argon-filled plasma
lenses that preserve beam emittance [C.A. Lindstr{\o}m et al., Phys. Rev. Lett.
121, 194801 (2018)]. Here we show that with argon in a 500 {\mu}m diameter
capillary, the fields are still linear with a focusing gradient of 3.6 kT/m,
which is an order of magnitude higher than the gradients of quadrupole magnets.
The current pulses that generate the magnetic field are provided by compact
Marx banks, and are highly repeatable. These results establish active plasma
lenses as an ideal device for pulsed particle beam applications requiring very
high focusing gradients that are uniform throughout the lens aperture.
