An exact perturbation expansion, to the order 1/S2, is derived for the Heisenberg ferromagnet. The equivalence of the Dyson-Maleev (DM), Holstein-Primakoff (HP) and matching-of-matrix-element (MME) transformations is proven. They give identical T5I2 and T4 coefficients. For the planar ferromagnet, an exact expansion in anisotropy against exchange field proves the equivalence of the H P and MME transformations. Several explicit results and numerical estimates are given.
Planar magnetron discharge is assisted by inductively coupled plasmas, which are sustained by a helical RF antenna immersed in the plasma. Use of the technique significantly enhances the plasma density. The effects of antenna termination when grounded or floating have been investigated by a simple circuit analysis. The floating antenna configuration effectively suppresses the anomalous rise of the plasma potential and thus the plasma source can be stably operated at a higher input of RF power to generate plasmas with densities as high as >1012 cm-3.
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