Abstract
A connection is established between two classical problems: the non linear saturation of a bump-on tail instability in collisionless regime, and the decay of a zonal flow towards a finite amplitude residual. Reasons for this connection are given and commented.
Highlights
This paper establishes a connection between two well-known analytical results that are currently used for code verification
In the case of the bump-on tail instability, it comes from the structure of the distribution function
In summary it is found that the saturation of a bump-on tail instability in collisionless regime, and the zonal-flow residual are connected
Summary
This paper establishes a connection between two well-known analytical results that are currently used for code verification. The second result addresses the saturated value of the bump-on tail instability in collisionless plasmas It predicts a bounce frequency of deeply trapped particles that is proportional to the linear growth rate, or equivalently a saturated mode amplitude that goes like the square of the linear drive (see [2] for an overview). This result is an extension of a seminal paper by O’Neil that addresses Landau damping in a nonlinear regime [3] (see the work by Mazitov [4]). It is flat within the island, and joins smoothly the unperturbed distribution function outside the separatrix This prescription is consistent with the detailed calculation of the mode evolution done by O’Neil in the same work.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
