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 ...