Theory of ions emitted from a plasma by relativistic self-focusing of laser beams

Abstract

Fast ions are emitted from the focus of a high-intensity laser beam irradiating a plasma. The selffocusing of the laser beam is caused by the dependence of the index of refraction on the relativistic mass of the electrons, which again depends on the electric-field strength. The ions are accelerated out of the laser focus due to the combined action of nonlinear forces and double layers. Results for the maximal energy and angular distribution of the ions are presented and compared with experimental data. PACS number(s): 52.40.Nk, 29.25. Cy, 52.25.Tx, 52.60.+h 4me n, CO ymHere, m, is the rest mass of the electron and n, the electron density. The relativistic Lorentz factor y depends on the electric-field strength E [5]. For example, the factor y is given for a circularly polarized wave of frequency co as 2 E2 1/2(2)The electric field of the very intense laser beam can be calculated by solving the nonlinear wave equation hE+ k E=O, derived from the Maxwell equations in certain approximations, where k =k (E)=n to /c and n is the refractive index of a noncollisional plasma depending on the plasma frequency given in Eq. (1):Analytical calculations of the self-focusing of a laser field penetrating a plasma were carried out by Hauser, Scheid, and Hora [6]. In these calculations we neglected the effects of collisions. Collisions were only found to have an inAuence near the low-intensity threshold and when the electron density is very close to the critical density Self-focusing of electromagnetic waves in a medium can arise if the index of refraction depends on the electric-field strength. In this case the effective radius of the laser beam decreases along the beam direction until it reaches a value of about a half wavelength of the incoming light. The theory of self-focusing was treated, for example, in the articles of Akhmanov, Sukhorukov, and Khokhlov [1], Svelto [2], Spatschek [3], and Hora [4].If a very intense laser beam (e.g., 10' W/cm for a Nd-glass laser with A, =1.06 pm) penetrates a plasma, relativistic self-focusing of the beam arises because of the relativistic velocity of the electrons which enters the relativistic mass of the electrons in the plasma frequency [5] e FNL= --, ' VE = -V(m, c y) . m, yco [4,5]. Since we assume that the threshold has been exceeded in the experiments considered in this Brief Report, we simply neglect the collisional implications in our treatment. An important consequence of relativistic self-focusing is the increase of the energy density of the laser field up to extremely high values in the region around the focal point. That means that nonlinear forces and double layers are developing which drive electrons and ions out of the focus region [4,7].The ions emitted from the focus can be accelerated up to energies of 10 MeV/nucleon depending on the laser intensity [8,9]. Therefore this effect can in principle be applied for the acceleration of particles by intense laser beams and has already been discussed under the name "laser focus accelerator" by Sessler [10], Hora et al. [11], and ...

Generation of extreme high laser intensities in plasma

“…Relativistic self-focusing [11], [12], [24], [25] is another spontaneous focusing mechanism that acts at much higher laser intensities (I rel = 3.66 × 10 18 /λ 2 W cm −2 ) [11], [24]), intensities at which the oscillatory quiver motion of the electrons in the laser field reaches energies in the range of mc 2 . The relativistic change of the electron mass causes a modification of the optical constants due to the relativistic intensity dependence of the absolute value of the refractive index n. An initially plane wavefront is thus bent into a concave wavefront, which tends to shrink down to a diffraction-limited beam diameter of about one wavelength.…”

“…The self-focusing length L sf has been calculated for a Nd:glass laser; it can be very long at low plasma density (N 1, N = n e /n cr ) [24], it is expected to be about 500 μm in [11], and it is very short (as low as two times the beam diameter) at the cut-off density, if the laser intensity is between 3 × 10 16 W cm −2 and 3 × 10 18 W cm −2 , [12], [24]. It has been stated in [24] that relativistic self-focusing also occurs at laser intensities that are much lower than the calculated relativistic threshold (10 −3 I rel is accepted in [12] and even lower intensities in [25]). Relativistic self-focusing is a fast process and starts immediately after the laser is switched on, whereas ponderomotive self-focusing arises later in time, when the electrons have moved out of the laser beam (10 −9 s [26]).…”

“…Relativistic self-focusing is a fast process and starts immediately after the laser is switched on, whereas ponderomotive self-focusing arises later in time, when the electrons have moved out of the laser beam (10 −9 s [26]). Ponderomotive self-focusing thus does not hinder relativistic self-focusing but contribute to the increase of the self-focusing effect [25].…”

Laser induced direct implantation of ions

“…Due to the presence of impurities the interpretation of this superfast group (e.g. relativistic self-focusing [20]) is problematic. We performed several experiments on implantation of Ag, Au, Pb, Sn and Ta ions into Al, Si, steel and plastic samples (e.g.…”

Experimental studies of interaction of intense long laser pulse with a laser-created Ta plasma

“…Following threshold intensity for relativistic self-focusing was derived [9] for a Nd:glass laser: I rel = 3.66 × 10 18 W/cm 2 and (since Iλ 2 ) is a similarity parameter), I rel = 3.66 × 10 16 W/cm 2 for a CO 2 laser. However, it has been stated [9] that the relativistic self-focusing also occurs at laser intensities much lower than the calculated relativistic threshold (10 −3 I rel is accepted in [11] and even lower intensities in [10,28]). The self-focusing length has been calculated for Nd:glass laser [8,9,11]: it can be very long at low plasma density (n e n cr ), [9], it is expected to be ∼ 500 µm in [8], and it is very short (as low as two times the beam diameter), if the laser intensity is between 3 × 10 16 and 3 × 10 18 W/cm 2 , [9,11].…”