Plasma models and rescaling methods

Abstract

The plasma models used in analytical or numerical studies exhibit, mainly for practical reasons, symmetry reducing the dimensions of the space. It is not obligatory that the restrictions on the dynamics and the chosen form of the electrostatic interactions should correspond to the same symmetry and this introduces the concept of a d (dynamic), d' (electrostatic) model with d' ≥ d. We show that the crucial parameter is d' – d. For d' – d = 0, the model exhibits both at low and at high temperature the same characteristic plasma frequency. At high temperature we recover the Vlasov limit and the plasma acts as a high-pass filter. For d' – d = 1, the two frequencies (purely collective at high temperature and ‘crystal’ frequency at very low temperature) are different, while in its high temperature (Vlasov) limit the plasma acts as a low-pass filter. Finally if d' – d ≥ 2 there is no longer a Vlasov limit for all values of temperature and density. These properties are obtained through a systematic use of the homothety transformations and a search for the corresponding invariants.