  High gradient quadrupoles are necessary for different applications such as
laser plasma acceleration, colliders, and diffraction limited light sources.
Permanent magnet quadrupoles provide a higher field strength and compactness
than conventional electro-magnets. An original design of permanent magnet based
quadrupole (so-called "QUAPEVA"), composed of a Halbach ring placed in the
center with a bore radius of 6 mm and surrounded by four permanent magnet
cylinders capable of providing a gradient of 210 T/m, is presented. The design
of the QUAPEVAs, including magnetic simulation modeling, and mechanical issues
are reported. Magnetic measurements of seven systems of different lengths are
presented and confirmed the theoretical expectations. The variation of the
magnetic center while changing the gradient strength is +/- 10 micrometer. A
triplet of three QUAPEVA magnets are used to focus a beam with large energy
spread and high divergence that is generated by Laser Plasma Acceleration
source for a free electron laser demonstration.
