Ultrahigh-intensity lasers are fundamental tools in modern physics. Their fast evolution over the last 15 years  started with the invention of chirped pulse amplification (CPA) . This technique opened a new window to the investigation of light-matter interactions. The CPA technique made it possible to generate much shorter laser pulses down to the femtosecond regime with laser peak powers reaching the 1–1000 terawatt level. Nowadays the most of the ultrahigh intensity lasers in the world are applying this method. One of these lasers is the Jena 12 TW laser . These lasers can be focussed down to a few micrometers and enormous intensities up to 1021 W/cm2 can be reached. At these intensities the electric field exceeds many times the binding energy of electrons in an atom. After a plasma is formed, the electrons oscillate at relativistic velocities in these fields . The interaction of ultrahigh-intensity laser pulses with plasmas became a central point of the investigations . There is a great variety of applications of these plasmas from particle acceleration, generation of electromagnetic waves to inertial confinement fusion. There is a large body of work about laser-plasma based electron acceleration . It was suggested originally in underdense plasmas by Tajima and Dawson . One type of these accelerators, the laser wakefield accelerator, is based on the generation of electron plasma waves and the electrostatic fields of these waves accelerates the electrons .