The authors have measured the sheath potential around a probe in a range of different plasma conditions in the UMIST quadrupole GOLUX and in a related experiment in which the plasma expands freely to supersonic velocity. In the latter case, the sheath potential agrees well with an appropriately modified form of the usual expression for a field-free plasma, for both hydrogen and argon plasmas. In GOLUX, however, the sheath potential is found to be significantly less than the accepted value, even when the magnetic field is taken into account. For the slow-moving plasma in the outer part of the quadrupole confining field, they present both theoretical and experimental results showing that the reduction is due to truncation of the electron velocity distribution as the probe drains electrons from a closed flux-tube faster than they can be replaced. In the central hot plasma, however, this explanation cannot apply. Here the plasma is moving at about sonic speed and magnetic effects are weak. Nevertheless the results are significantly different from those in the field-free experiment.

The relativistic self-focusing of an intense laser beam, propagating in a plasma transverse to the ambient magnetic field, has been studied using the slab model. The laser propagates in the extraordinary mode with Gaussian distribution of intensity in one transverse dimension and focuses in a periodic manner on the distance of propagation. The extent of self-focusing increases with increasing magnetic field. Both the minimum spot size and the self-focusing length decrease with magnetic field.

In this work, the problem of relativistic self-focusing of a q-Gaussian laser beam propagating in unmagnetized plasma is studied using a simple heuristic approach. The q-Gaussian profile is analyzed with respect to full width at half maximum (FWHM), intensity distribution, and critical power. A modified version of the Akhmanov method is used to solve the non-linear differential equation for the q-Gaussian beam. The results showed that the FWHM of the q-Gaussian beam substantially depends on the q-factor, and for high values of q, a small part of the beam energy becomes contained within the FWHM. The q-parameter is more effective in the diffraction term than the nonlinear term. The critical power of the q-Gaussian laser beam needed for self-focusing as q→1 becomes extremely high, and in this case, it is very hard to wave-guide such a beam. Moreover, the critical power of self-focusing for q-Gaussian is highly dependent on the value of q-parameter, and as q goes to zero, the critical power needed for self-focusing becomes extremely high. All the derived expressions for the q-Gaussian beam become identical to those for a normal Gaussian beam as q approaches to infinity.

In this paper, plasma is generated from the nano and bulk copper targets by using Nd:YAG laser with a wavelength of 1064 nm, frequency of 6 Hz and pulse duration 9 ns at atmospheric pressure. The Boltzmann plot method was used to calculate the temperature of electrons and the Stark broadening method to calculate the density of electrons in a laser-generated plasma. It was observed that increased in the laser energy from 500 to 800 mJ leads to increased the temperature of electrons from 1.8 to 2.5eV and increased the electrons density from 3.65×1016 to 4.29×1016 cm−3 for nano copper plasma while increased the temperature of electrons from 1.2 to 2 eV and increased the electrons density from 2.28×1016 to 3.24×1016 cm−3 for the bulk copper plasma.

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