## 3 Applications with J-KAREN Laser System
### Prospects of High Field Science Experiments  
Nowadays with the fast growth of laser intensity it was realized that it can be used to probe an unexplored regime of interaction of charged particles with radiation and the properties of the vacuum [90, 103, 104]. The probabilities of the processes in high intensity electromagnetic (EM) fields involving electrons, positrons, and photons depend on three parameters (see details in [105]):  
\[a=\frac{eE}{m_{e}\omega c},\ \ \ \varepsilon_{nd}=\frac{2\omega r_{e}}{3c},\ \ \ \chi_{e}=\frac{\sqrt{\left(F^{\, \mu\
u}\,p_{\
u}\right)^{2}}}{m_{e}cE_{S}},\ \ \ \ \chi_{\gamma}=\frac{\hbar\sqrt{\left(F^{\, \mu\
u}k_{\
u}\right)^{2}}}{m_{e}cE_{S}}. \tag{1}\]  
where \(e\) and \(m_{e}\) are the charge and mass of an electron, \(\mathrm{c}\) is the speed of light, \(\hbar\) is Planck constant, \(\omega\) and \(E\) are the EM field frequency and strength, respectively, \(r_{e}=e^{2}\,/\,m_{e}c^{2}=2.8\times 10^{-13}\,\mathrm{cm}\) is the classical electron radius, \(F^{\,\mu\
u}\) is the tensor of the EM field, and \(p^{\
u}\) and \(\hbar k^{\
u}\) are the electron, positron and photon momentum. The first parameter, \(a\), is the dimensionless amplitude of the EM field, and is purely classical parameter. It has a meaning of electron energy gain over a distance of \(\lambda=c/\omega\) in units of its rest energy, \(m_{e}c^{2}\). When \(a\) is small the most probable are the processes with minimum possible number of photons. At \(a<<1\) the probabilities become equal to the perturbation theory probabilities and plane waves represents an ensemble of individual photons. The linear regime of photon-electron (Thomson) scattering (see for example [106]) mentioned here is of a paramount importance for the generation of gamma-rays sourced for nuclear applications, both for accelerator based sources and also for laser based sources. When \(a\approx 1\) or \(a>>1\) the probabilities of absorbing different number of photons become comparable and the process becomes multiphoton, _i.e._, the probability has an essentially nonlinear dependence on the field. With the rapid development of laser technology EM pulses routinely obtain \(a>>1\). The EM pulse with the intensity corresponding to \(a\) above 30 has been generated by the J-KAREN laser system used in the experiments [19]. The second parameter \(\varepsilon_{rad}\) characterizes the radiation friction effects. At the laser field amplitude above \(a_{rad}=\varepsilon_{rad}^{-1/3}\approx 400\), corresponding to \(10^{23}\) W/cm\({}^{2}\), the radiation friction makes the laser-matter interaction highly dissipative. This results in the high power gamma-ray flash generation [107]. The third parameter \(\chi_{e}\) has a meaning of the ratio of EM field strength in the rest frame of the particle to the critical QED field equal to  
\[E_{S}=\frac{m_{e}^{2}c^{3}}{e\hbar}=1.32\times 10^{16}\,\mathrm{V/cm} \tag{2}\]  
The field \(E_{S}\) produces a work over the Compton wavelength distance of \(\lambda_{c}=\hbar/\,m_{e}c=3.86\times 10^{-11}\,\mathrm{cm}\) equal to \(m_{e}c^{2}\). Parameters \(\chi_{e}\) and \(\chi_{\gamma}\) are responsible for the magnitude of the quantum nonlinear effects: when \(a>>1\) these effects are maximized for \(\chi_{e,\gamma}\approx 1\). All these processes in high intensity EM fields are part of a new emerging branch of physics. There are two principle experimental schemes aimed at the study of fundamental physics effects at high laser intensity [105, 108]: (a) colliding laser pulses (all optical setup) and (b) laser-electron beam interaction. The first one could be employed for the study of direct vacuum breakdown, _i.e._, the electron-positron pair production under the action of intense EM field and the subsequent \"avalanche\". The second scheme will allow for the study of basic processes: photon emission by an electron and a photon conversion into an electron-positron pair in intense EM field.