Plasma Heating Due to Cyclic Diffusion Across a Separatrix*

Particles crossing separatrices are ubiquitous in plasmas. This work presents the first definitive observation of heating due to collisional separatrix crossing in a plasma with heating scaling as the square root the collision rate. This “classic” result was theoretically predicted by Galeev in 1969 [1], Rosenbluth in 1972 [2], Minick 2006 [3] and more recently Dubin[4]; but never observed directly in a plasma.

We observe this dissipative separatrix heating when a pure ion plasma column is forced back and forth across a partial trapping barrier. The barrier is an externally applied axisymmetric “squeeze” potential, imposed to create a velocity separatrix between trapped and passing particles. Trapped particles can only explore a limited section of phase space whereas passing particles can explore the entire phase space.
Weak collisions then cause separatrix crossings, leading to irreversible heating in each forcing cycle. The heating rate scales as the square root of the collision frequency times the oscillation rate, and thus is large for low-collisionality plasmas. 

The particle velocity distribution function is measured with Coherent Laser Induced Fluorescence, and shows passing and trapped particles having an out-of-phase response to the forced plasma oscillations, in quantitative agreement with recent collisionless adiabatic invariant analysis.

“Synthetic” collisions from externally applied electrostatic noise cause velocity diffusion and thus enhanced separatrix crossings, with resultant heating also observed to scale as square root of the synthetic collisions rate.

 

[1] A. A. Galeev,et. al., PRL, 22, 511 (1969)

[2] M.N. Rosenbluth, D.W. Ross, D.P. Kostomarov, Nuclear Fusion, 12, 3 (1972)

[3] H. Mynick, Physics of Plasmas, 13, 058102 (2006)

[4] D.H.E. Dubin, Physics of Plasmas, 24, 112120 (2017)