Resonant heating of particles by electrostatic and Alfvén waves propagating in a confining uniform magnetic field is examined. It is shown that, with a sufficiently large wave amplitude, significant perpendicular stochastic heating can be obtained with wave frequency at a fraction of the cyclotron frequency. This result may have relevance for the heating of ions in the solar corona, and is a generic phenomenon, independent of the type of wave considered.

Resonant heating of a magnetized plasma by low frequency waves of large amplitude is considered. It is shown that the magnetic moment can be changed nonadiabatically by a single large amplitude wave, even at frequencies normally considered nonresonant. Two examples clearly demonstrate the existence of the resonances leading to chaos and the generic nature of heating below the cyclotron frequency. First the classical case of an electrostatic wave of large amplitude propagating across a confining uniform magnetic field, and second a large amplitude Alfvén wave, propagating obliquely across the magnetic field. Waves with frequencies a small fraction of the cyclotron frequency are shown to produce significant heating; bringing, in the case of Alfvén waves, particles to speeds comparable to the Alfvén velocity in a few hundred cyclotron periods. Stochastic threshold for heating occurs at significantly lower amplitude with a perturbation spectrum consisting of a number of modes. This phenomenon may have relevance for the heating of ions in the solar corona as well as for ion heating in some toroidal confinement fusion devices.

a b s t r a c tThe purpose of this work is to improve the precision of the elemental analysis of coal using laserinduced breakdown spectroscopy (LIBS). The LIBS technique has the ability to allow simultaneous elemental analysis and on-line determination, so it could be used in the elemental analysis of coal. Organic components such as C, H, O, N and inorganic components such as Ca, Mg, Fe, Al, Si, Ti, Na, and K of coal have been identified. The precision of the LIBS technique depends strongly on the experimental conditions, and the choice of experimental parameters should be aimed at optimizing the repeatability of the measurements. The dependences of the relative standard deviation (RSD) of the LIBS measurements on the experimental parameters including the sample preparation parameters, lensto-sample distance, sample operation mode, and ambient gas have been investigated. The results indicate that the precision of LIBS measurements for the coal sample can be improved by using the optimum experimental parameters.