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

Advances in Optics, Photonics, Spectroscopy & Applications VI ISSN 1859 - 4271Fig. 7. Two-dimensional simulation of laser pulse propagation in plasma.The Hamiltonian of the electrons under the electromagnetic field is written as H = [p-(e/c)A(r,t)] 2 /2m, where p is the momentum of the electrons and A is the vector potential of the field.The time average of H is given by = p 2 /2m + e 2 A 2 (r)/4mc 2 . The second term in the righthand side U P = e 2 A 2 (r)/4mc 2 , the extra energy the electrons gain in the field, is called ponderomotivepotential. This is written as U P = 100keV x I (10 18 W/cm 2 ) λ 2 (µm). At the intensity ofI=10 20 W/cm 2 , it reaches to U P ~6.2 MeV for λ =790 nm. When the laser beam is focused intothe plasma, the electrons are expelled from the high intensity region (beam center) to the lowerintensity region (outside the laser beam) due to the pondero-motive energy, forming the ionchannel along the laser propagation.In the relativistic region, the electron mass m depends on its velocity v as m = m 0 /[1-(v 2 /c 2 )] 1/2 ~ m 0 [1+a 0 2 ] 1/2 , where is m 0 the electron rest mass. The plasma frequency ω p dependson the electron density n 0 and the electron mass m as ω p = [4πn 0 e 2 /m] 1/2 = ω p0 /[1+ a 0 2 ] 1/4 , whereω p0 =[4πn 0 e 2 /m 0 ] 1/2 is the plasma frequency without the laser field. The refractive index of theplasma is given by η = [1- ω p 2 / ω 2 ] 1/2 .For the Ti:sap<strong>ph</strong>ire laser focused to the intensity of I=10 20 W/cm 2 , corresponding to a 0 ~6.7,the electron mass increases by m~6.8m 0 , the plasma frequency decreases by ω p ~ ω p0 //2.6, andthe refractive index increases from η=0.86 to 0.98 (14 %) for an underdense plasma of n 0 =n c /4,i.e. ω p0 = ω/2, where n c is the critical density. Due to increase in the refractive index, the laserbeam propagates in a plasma channel formed by self-focusing in the plasma.The relativistic effect in plasma has been successfully applied to acceleration of electrons tohigh energies [9]. Figure 7 shows the 2-dimentional simulation of the propagation of a highintensity, short laser pulse in plasma [10,11]. A cavity is formed in the plasma due to theponderomotive potential of the laser pulse. The electrons expelled at the front of the cavity bythe intense laser field turns around the cavity and injected to the backside of the cavity. Theelectrons are accelerated by the extremely high electric field produced by the wake wave whichmoves close to the light velocity since it is formed by the laser pulse propaga<s<strong>trong</strong>>tin</s<strong>trong</strong>>g in the plasma.With the acceleration distance of a cm scale, a mono-energetic, highly collimated electron beamof 1 GeV energy has been generated by propaga<s<strong>trong</strong>>tin</s<strong>trong</strong>>g a 40 TW laser pulse in a 3.3-cm-longcapillary discharge waveguide [12]. Since the electric field generated with the laser wake is 10 3-4times higher than the field with the standard microwave cavity accelerator, the laser wakefieldaccelerator has a possibility to make the electron accelerator a very compact device.V. NONLINEAR PROCESSES IN VACUUMDirac has shown that electrons have both positive and negative energy states [13]. Vacuum isthe state where all the negative energy states are filled. When an electron with positive energy e -is created from the vacuum, the vacancy state acts as a positively charged particle e + which iscalled positron. The minimum energy to create the electron-positron pair is 2mc 2 , since the24