Turbulence acceleration by strong Langmuir plasmons in a laser-plasma

The turbulence acceleration of ultra-relativistic electrons by strong Langmuir plasmons is analytically studied in a laser-plasma. Based on the Fokker-Planck equation in the frame of strong turbulence, the exponential form of the spectra of hot electrons is obtained theoretically, which is consistent with the experimental result near the critical surface in a laser-plasma.