Flux Jamming, Phase Transitions and Layering in Turbulent Magnetized Plasma

TL;DR

This paper investigates how jam formation in avalanching drift-wave turbulence leads to layering and transport barriers, drawing deep analogies to one-dimensional traffic flow and motility-induced phase separation (MIPS). It identifies two routes to heat-flux jamming: a rollover of the heat-flux function $Q_T(\delta T)$ with $dQ_T/d\delta T<0$, and a finite relaxation-time effect $\tau_R$ that slows the flux response, both of which can generate jamitons and staircase profiles. The authors develop a hierarchy of models from kinematic-wave formulations to dynamic, diffusion-influenced equations, including a nonlinear telegraph equation, and extend the framework to particle flux with the Hasegawa-Wakatani system, showing robust jam-driven layering and critical avalanche statistics near marginality. The work highlights the role of turbulence spreading and transport barriers in shaping confinement, and provides a unifying language to describe jamming, staircase formation, and phase-like transitions in magnetized plasma transport.

Abstract

This paper discusses transport barrier formation and layering as consequences of jam formation. Extensive use is made of analogies with the theory of traffic flow in one dimension. The relation of flux jamming to motility induced phase separation (MIPS) is explained. Two routes to heat flux jamming are identified. The first is due to a rollover in the heat flux-pulse size relation, i.e. $dQ_T(δT)/dδT<0$, and is similar to the condition of flux-gradient bistability. The second occurs when the delay time between pulse and heat flux exceeds a critical value. This does not require bistability and tends to occur near marginality. This analysis yields an estimate of the answer to the eternal question of 'how near is "near"?'. Staircase development is shown to follow jamiton train formation. The relation of jamming of avalanches to phase transitions in drift wave-zonal flow turbulence is elucidated. The formation of outward propagating blob trains and inward propagating void trains is demonstrated. The important role of turbulence spreading is identified.

Figures (17)

• Figure 1: Approaches to Jam
• Figure 2: A cartoon for an avalanche event. Also shown are relevant length scales, i.e. cell size $\Delta$, event size $l$ and the system size $L$.
• Figure 3: Outgoing blob and incoming void
• Figure 4: An example of u-shaped flux. For large $\delta T$, the flux decreases, i.e. $dQ/d\delta T<0$. The rollover is a route for various relevant phenomena, such as transport bifurcation, jamming, etc, as explained in detail in the text.
• Figure 5: Forward and backward shocks