LAWS FOR ELECTRON PRESSURE VARIATIONS ACROSS A COLLISIONLESS SHOCK

In order to characterize the electron pressure variations across an ob lique collisionless shock, statistical methods are applied to the resu lts of two-dimensional (2-D) full particle electromagnetic simulations . Local correlations are looked for between the spatial variations of the pressures p(parallel to) and p(perpendicular to) (parallel and per pendicular to the local magnetic field) throughout the shock profile a nd the corresponding variations of the density n and the magnetic fiel d modulus B at the same location. Different orders in regression laws are successively analyzed, including me most general 4-D regressions p (perpendicular to)p(parallel to)(-u)n(-v)B(-2w) = constant, which test the degree of invariance of the quantities p(perpendicular to)p(paral lel to)(-u)n(-v)B(-2w), the reduced 3-D laws p(perpendicular to)n(-a p erpendicular to)B(-2b perpendicular to) = cst, p(parallel to)n(-a para llel to)B(-2b parallel to) = cst (as in CGL theory), and the reduced 2 -D correlations laws p perpendicular to n(-gamma perpendicular to) = c st, p(parallel to)n(-gamma parallel to) = cst, nB(-Cp) = cst (polytrop ic forms). Coefficients are determined quantitatively for each law. Th e use of these different regressions laws allows to check(1) where loc al correlations between these four quantities do exist at a given scal e and, when verified, what is their effective forms; (2) when these ge neral closure laws can be reduced to simpler ones, in particular to po lytropic forms and with which polytropic indexes (gamma=5/3?). This la st result may have consequences concerning the fluid plasma modelizati ons for collisionless shocks or other nonlinear configurations; a comp arison with the existing theories about the closure of fluid equations is briefly presented.