“…In direct electron acceleration in vacuum, it was difficult to produce high-density electron bunches, because the laser transverse ponderomotive force scatters the electrons in the perpendicular direction of the laser propagation (10)- (15) . This electron density reduction can be suppressed by a laser composed of a linear combination of the Hermite-Gaussian TEM 10 and TEM 01 modes with the orthogonal polarization (13)- (15) . The transverse electric field of the TEM 10 +TEM 01 mode laser propagating in the z direction is written by E(x, y, z, t)=E 1,0 (x, y, z, t)e x +E 0,1 (x, y, z, t)e y .…”