Recently, it was shown that certain 'smart' self-avoiding trails have end-to-end distances R 2 N ∼ N in three dimensions. Also, the corrections to scaling of R 2 N /N and the specific heat are qualitatively very similar to those for polymers exactly at the θ point. The question was thus posed whether they are in the same universality class as linear polymers at the θ temperature. We show that this is not the case since these trails show a first-order transition, instead of the second-order transition at the usual θ point. We argue that this is due to the fact that the 'smartness' of these trails implies that the renormalized n-body interactions vanish identically for any finite n 3. We conjecture that the qualitative similarity with recent simulations of θ polymers indicates that for n-body interactions the renormalized three-body interaction is small in real polymers.

In spite of the fact that the petawatt level has been attained quite a time ago [ 1 ], only a few petawatt facilities are available worldwide. One of them, a 056 PW OPCPA facility, was created at the Institute of Applied Physics in 2006 [2]. The main OPCPA merit is a possibility of power scaling . In the current work we report construction of still another Russian OPCPA-based laser complex.A 100 TW laser [ 3 ] was taken as a front-end system supplemented with one more cascade of parametric amplification -a KD*P crystal with clear aperture of 20xlO em. One channel of "Luch" facility (RFNC -VNIIEF, Sarov) [ 4] with 2 kJ output pulse energy at the wavelength of 1054 nm was used as a pump laser. A 1 kJ pulse having duration 2.3 ns at the second harmonic is used to pump the [mal stage of the parametric amplifier. Maximum energy obtained in a chirped pulse is more than 100 J ( fig. la). Autocorrelation function on compression is shown in fig. 1b. If the pulse shape is regarded to be Gaussian , then its duration is 70 fs, which corresponds to the power of 1 PW at compressor output. Beam divergence is close to diffraction limit ( fig. lc). (a) (b) (c) 120 100 0 ;;, 0 -80 s 0 1i 60 -= ore 0. '0 40 n~_~_ " e-I---20 o -rko0 _0 0 I o -----t-f 0 600 pump ene rgy , J 1200 1 Fig. 1 Dependence of chirped pulse energy on OPCPA pump energy (a), autocorrelation function (b), and far field distribution (c) oflPW beam.Perspectives of a further increase of laser power using OPCPA in a KD*P crystal are considered. There may be different ways of increasing power: i) pump power enhancement either using glass with high nonlinear refractive index or increasing amplifier aperture; ii) increase of the efficiency of parametric amplification, and iii) shortening of pulse duration as a result of which a KD*P crystal amplifies pulses with the spectrum corresponding to the duration of 10-15 fs.Other channels of"Luch" facility may also be employed as additional pump of parametric amplifier(s). References[II

A study of the maximal intensity peaks due to nonlinear holographic images of obstacles such as obscurations or phase defects in a high-power laser system is presented. It is shown that the interference of the high-power plane wave and the converging image wave results in the formation of intensity maximums in the vicinity of the image plane, the values of which significantly exceed the intensity in the image plane itself. For round obstacles, analytical expressions that describe magnitudes and locations of the maxima depending on the radius and the type of obstacle are given. A procedure of numerical modeling that allows estimation of the influence of beam size, medium thickness, type, size, and shape of obstacles onto the properties of nonlinear images is described. It is demonstrated that for a given combination of the nonlinear medium and the high-power beam parameters, there is an intrinsic size of obstacles that is most harmful for the laser system components.

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