**6. Acknowledgements**

The authors are grateful to Philip J. Morrison of the Institute for Fusion Studies of the University of Texas in Austin, for useful discussions and criticism. The work of Massimo Materassi has been partially supported by EURATOM through the "Contratto di Associazione Euratom-Enea-CNR". The work of Emanuele Tassi was partially supported by the Agence Nationale de la Recherche (ANR GYPSI n. 2010 BLAN 941 03). This work was also supported by the European Community under the contract of Association between EURATOM, CEA, and the French Research Federation for fusion study. The views and opinions expressed herein do not necessarily reflect those of the European Commission. Emanuele Tassi acknowledges also fruitful discussions with the "Equipe de Dynamique Nonlinéaire" of the Centre de Physique Théorique of Marseille.

Giuseppe Consolini and Massimo Materassi did this work as a part of ISSI Team n. 185 "Dispersive cascade and dissipation in collisionless space plasma turbulence – observations and simulations", lead by E. Yordanova.
