Two caravans travel toward each other along a narrow road. One is wide and slow, carrying a load of density. The other, a string of light carts carrying current, slips between the first. Thus, in a magnetron discharge, two structures rotating in opposite directions coexist: the density spoke and the current filaments.
For a long time, it was unclear how the large-scale rotating spoke and small-scale turbulence together create anomalous electron transport across the magnetic field. They built the first three-dimensional kinetic model of a magnetron discharge, one where each electron and ion is tracked individually, like caravan drivers on the road. The calculation reproduced the measured spoke: the density rotates in the −E×B direction at 90 kHz, while the current filaments rotate in the +E×B direction at 1.0 MHz.
Now we can see how the two caravans share the road. In the plasma bulk, the spoke (modes m=1–3) carries 96.7% of the transverse flux. At the sheath boundary, turbulence (modes m=12–22) takes over exactly half. On the intermediate line, the spoke is still ahead, at 63.7%. This is not just coexistence, but a redistribution of roles as one approaches the wall.
The caravans move toward each other but do not hinder one another; they exchange energy with almost no net heating. It is precisely this exchange that sustains ionization at the spoke front. The results are applicable to optimizing magnetron sputtering and Hall thrusters, where anomalous transport determines efficiency. Two opposing flows on the same road turned out not to be an obstacle, but the engine of the discharge.
The rotation frequency of current filaments, 1 MHz, is a hundred times higher than the spoke frequency of 10 kHz, yet both structures coexist in the same discharge and modulate each other.