  Laser Plasma Acceleration (LPA) is capable of producing a GeV beam within a
cm accelerating distance, but with a rather high initial divergence and large
energy spread. COXINEL aims to demonstrate a compact Free Electron Laser using
such a source, where a specific transport line with adequate elements is used,
such as tunable high gradient quadrupoles for handling the divergence. An
innovative permanent magnet based quadrupole (QUAPEVA) made of two quadrupoles
superimposed capable of generating a gradient of 200 T/m is presented. The
first quadrupole consists of magnets shaped as a ring and attaining a constant
gradient of 155 T/m, and the second one made of four cylindrical magnets
surrounding the ring and capable of rotating around their axis to achieve a
gradient tunability of $\pm$ 46 T/m. Each tuning magnet is connected to a motor
and controlled independently, enabling the gradient to be tuned with a rather
good magnetic center stability ($\pm$10 $\mu$m) and without any field
asymmetry. The measurements and field optimization of seven quadrupoles with
different magnetic lengths are reported. A set of QUAPEVA triplet, installed at
COXINEL, achieved good focusing and enabled beam based alignment.
