Past exam of the mathematics course of the University of Cambridge 2006 iii Paper 69 2 d Solution Created 2026-10-03 Updated 2026-10-14
Critical balance makes the nonlinear interaction time comparable to the wave period:An order-one interaction transfers energy in , so constant energy flux gives . Thus the critically balanced electron-magnetohydrodynamic cascade hasFor the corresponding perpendicular magnetic energy spectrum, gives . The increasing ratio describes progressively more anisotropic fluctuations at smaller perpendicular scales, within the range in which the model and critical balance assumptions hold.