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It is possible that strong collisionless damping can lead to a broadening of the three-wave resonances constraining weak turbulent interactions and this effect might lead to a parallel cascade of kinetic Alfvén waves in the weak turbulence limit. Nonlinear kinetic simulations focused on this problem will likely be able to settle this question. Until evidence is found in support of this possibility, however, we maintain the conjecture the weak kinetic Alfvén wave turbulence generates no parallel cascade.
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