Nhng tin b trong Quang hc, Quang ph và ng dng VI ISSN 1859 - 4271

Những tiến bộ <strong>trong</strong> <strong>Quang</strong> học, <strong>Quang</strong> <strong>ph</strong>ổ và Ứng dụng VI ISSN 1859 - 4271IV. RELATIVISTIC PHENOMENA IN PLASMASWhen a high power laser beam is focused to a small spot, the electric field at the focusbecomes very high. From the relation I=E 2 /(2Z 0 ) where Z 0 =337 Ω, the electric field E isexpressed with the intensity I as E (V/m) = 2.6x10 3 [I (W/cm 2 )] 1/2 . For example, E=26 V/A at theintensity of I=10 16 W/cm 2 . This field is comparable to the Coulomb field of E=26 V/A for theground state electron of hydrogen. Therefore the atoms are almost completely ionized when thelaser intensity far exceeds ~10 16 W/cm 2 and the medium becomes the plasma state which iscomposed of free electrons and ions.The electron motion under the optical field is described asmdv/dt = F = e[E+(v/c)xB], (1)where m is the electron mass, v is the electron velocity, F is the force to the electron, c is thevelocity of light in vacuum and B is the magnetic field. For the electric field of E = E 0 sin ωt, theelectron motion is described as v = -(eE 0 /mω) cos ωt, since the second term on the right handside of eq. (1) is smaller than the first term when v«c. From this relation, the electron velocitybecomes comparable to the light velocity c, when the normalized electric fielda 0 = eE 0 /mcω = 0.85 λ (µm) Ι 1/2 (10 18 W/cm 2 ) (2)is close to unity. From this relation, v ~ c at the laser intensity of I=10 18 W/cm 2 for the laser ofλ∼1 µm wavelength such as a Ti:sap<strong>ph</strong>ire laser of λ =790 nm. At the higher intensity ofI=10 20 W/cm 2 , a 0 ~6.7 for λ =790 nm.The relativistic effects become important when the electron velocity becomes close to thevelocity of light. For example, the absolute value of the second term on the right hand side of eq.(1) becomes close to the first term. When v « c, the electron oscillates in the direction of theelectric field E as shown in a of Fig. 6. Since the force to the electron F ~ v x B is in the zdirection, the electron motion in the z-direction is superposed to the oscillation in the x direction.When the laser intensity is very high, the electron moves in the forward direction as shown in bof Fig. 6.Fig. 6. Electron motions at a 0